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Selina solutions for Concise Mathematics Class 10 ICSE chapter 21 - Trigonometrical Identities [Latest edition]

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Concise Mathematics Class 10 ICSE - Shaalaa.com

Chapter 21: Trigonometrical Identities

Exercise 21(A)Exercise 21(B)Exercise 21(C)Exercise 21(D)Exercise 21(E)

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise Exercise 21(A) [Pages 324 - 325]

Exercise 21(A) | Q 1 | Page 324

Prove.
`(secA-1)/(secA+1)=(1-cosA)/(1+cosA)`

Exercise 21(A) | Q 2 | Page 324

Prove.
`(1+sinA)/(1-sinA)=(co   secA+1)/(co   sinA-1`

Exercise 21(A) | Q 3 | Page 324

Prove.
`1/(tanA+cotA)=cosAsinA`

Exercise 21(A) | Q 4 | Page 324

Prove.
`tanA-cotA=(1-2cos^2A)/(sinAcosA)`

Exercise 21(A) | Q 5 | Page 324

Prove.
`sin^4A-cos^4A=2sin^2A-1`

Exercise 21(A) | Q 6 | Page 324

Prove.
`(1-tanA)^2+(1+tanA)^2=2sec^2A`

Exercise 21(A) | Q 7 | Page 324

Prove.
cosecA - cosec2 A = cot4 A + cot2 A

Exercise 21(A) | Q 8 | Page 324

Prove.
sec A (1-sin A) (sec A + tan A) = 1

Exercise 21(A) | Q 9 | Page 324

Prove.
cosec A(1+ cos A) (cosecA - cot A) =1

Exercise 21(A) | Q 10 | Page 324

Prove.
sec2 A + cosec2 A = sec2 A cosec2 A

Exercise 21(A) | Q 11 | Page 324

Prove.
`((1+tan^2A)cotA)/(cosec^2A)=tanA`

Exercise 21(A) | Q 12 | Page 324

Prove.
tan2A - sin2A = tan2A sin2A

Exercise 21(A) | Q 13 | Page 324

Prove.
cot2 A - cos2 A = cos2 A.cot2 A

Exercise 21(A) | Q 14 | Page 324

Prove.
(cosec A + sin A) (cosec A - sin A) = cot2 A + cos2

Exercise 21(A) | Q 15 | Page 324

Prove.
(sec A - cos A) (sec A + cos A) = sin2 A + tan2

Exercise 21(A) | Q 16 | Page 324

Prove.
(cosA + sinA)2 + (cosA - sinA)2 = 2

Exercise 21(A) | Q 17 | Page 324

Prove.
(cosec A - sin A) (sec A - cos A) (tan A + cot A) = 1

Exercise 21(A) | Q 18 | Page 324

Prove.
`1/(sec A+tanA)=secA-tanA`

Exercise 21(A) | Q 19 | Page 324

Prove.
`cosecA+cotA=1/(cosecA-cotA)`

Exercise 21(A) | Q 20 | Page 324

Prove.
`(secA-tanA)/(secA+tanA)=1-2secAtanA+2tan^2A`

Exercise 21(A) | Q 21 | Page 324

prove.
(sinA + cosecA)2 + (cosA + secA)2 = 7 + tan2A + cot2A

Exercise 21(A) | Q 22 | Page 324

prove.
sec2A cosec2A = tan2A + cot2A + 2

Exercise 21(A) | Q 23 | Page 324

Prove.
`1/(1+cosA)+1/(1-cosA)=2cosec^2A`

Exercise 21(A) | Q 24 | Page 324

Prove.
`1/(1-sinA)+1/(1+sinA)=2sec^2A`

Exercise 21(A) | Q 25 | Page 324

Prove.
`(cosecA)/(cosecA-1)+(cosecA)/(cosecA+1)=2sec^2A`

Exercise 21(A) | Q 26 | Page 324

prove.
`secA/(secA+1)+secA/(secA-1)=2cosec^2A`

Exercise 21(A) | Q 27 | Page 324

Prove.
`(1+cosA)/(1-cosA)=tan^2A/(secA-1)^2`

Exercise 21(A) | Q 28 | Page 324

Prove.
`cot^2A/(cosecA+1)^2=(1-sinA)/(1+sinA)`

Exercise 21(A) | Q 29 | Page 324

Prove.
`(1+sinA)/cosA+cosA/(1+sinA)=2secA`

Exercise 21(A) | Q 30 | Page 325

Prove.
`(1-sinA)/(1+sinA)=(secA-tanA)^2`

Exercise 21(A) | Q 31 | Page 325

Prove.
`(cotA-cosecA)^2=(1-cosA)/(1+cosA)`

Exercise 21(A) | Q 32 | Page 325

Prove.
`(cosecA-1)/(cosecA+1)=(cosA/(1+sinA))^2`

Exercise 21(A) | Q 33 | Page 325

Prove.
`tan^2A-tan^2B=(sin^2A-sinB)/(cos^2Acos^2B`

 

Exercise 21(A) | Q 34 | Page 325

Prove.
`(sinA-2sin^3A)/(2cos^3A-cosA)=tanA`

Exercise 21(A) | Q 35 | Page 325

Prove.
`sinA/(1+cosA)=cosecA-cotA`

Exercise 21(A) | Q 36 | Page 325

Prove.
`cosA/(1-sinA)=secA+tanA`

Exercise 21(A) | Q 37 | Page 325

Prove.
`(sinAtanA)/(1-cosA)=1+secA`

Exercise 21(A) | Q 38 | Page 325

Prove.
(1 + cot A - cosec A)(1+ tan A + sec A) = 2 

Exercise 21(A) | Q 39 | Page 325

Prove.
`sqrt((1+sinA)/(1-sinA))=secA+tanA`

Exercise 21(A) | Q 40 | Page 325

Prove.
`sqrt((1-cosA)/(1+cosA))=cosecA-cotA`

Exercise 21(A) | Q 41 | Page 325

Prove.
`sqrt((1-cosA)/(1+cosA))=sinA/((1+cosA)`

 

Exercise 21(A) | Q 42 | Page 325

Prove.
`sqrt((1-sinA)/(1+sinA))=cosA/(1+sinA)`

Exercise 21(A) | Q 43 | Page 325

Prove.
`1-cos^2A/(1+sinA)=sinA`

Exercise 21(A) | Q 44 | Page 325

Prove.
`1/(sinA+cosA)+1/(sinA-cosA)=(2sinA)/(1-2cos^2A)`

Exercise 21(A) | Q 45 | Page 325

Prove.
`(sinA+cosA)/(cosA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(2sin^2A-1)`

Exercise 21(A) | Q 46 | Page 325

Prove.
`(cotA+cosecA-1)/(cotA-cosecA+1)=(1+cosA)/sinA`

Exercise 21(A) | Q 47 | Page 325

Prove.
`(sinthetatantheta)/(1-costheta)=1+sectheta`

Exercise 21(A) | Q 48 | Page 325

Prove.
`(costhetacottheta)/(1+sintheta)=cosectheta-1`

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise Exercise 21(B) [Page 327]

Exercise 21(B) | Q 1.1 | Page 327

Prove.
`cosA/(1-tanA)+sinA/(1-cotA)=sinA+cosA`

Exercise 21(B) | Q 1.2 | Page 327

Prove.
`(cos^3A+sin^3A)/(cos^3A+sin^3A)+(cos^3A-sin^3A)/(cos^3A-sin^3A)=2`

Exercise 21(B) | Q 1.3 | Page 327

Prove.
`tanA/(1-cotA)+cot/(1-tanA)=secA cosecA+1`

Exercise 21(B) | Q 1.4 | Page 327

Prove.
`(tanA+1/cosA)^2+(tanA-1/cosA)^2=2((1+sin^2A)/(1-sin^2A))`

Exercise 21(B) | Q 1.5 | Page 327

Prove.
 2 sin2A + cos4A = 1 + sin4

Exercise 21(B) | Q 1.6 | Page 327

Prove.
`(sinA-sinB)/(cosA+cosB)+(cosA-cosB)/(sinA+sinB)=0`

Exercise 21(B) | Q 1.7 | Page 327

Prove.
`(cosecA-sinA)(secA-cosA)=1/(tanA+cotA)`

Exercise 21(B) | Q 1.8 | Page 327

Prove.
(1 + tanA tanB)2 + (tanA - tanB)2 = sec2A sec2

Exercise 21(B) | Q 1.9 | Page 327

Prove.
`1/(cosA+sinA-1)+1/(cosA+sinA+1)=cosecA+secA`

Exercise 21(B) | Q 2 | Page 327

If x cos A + sin A = m and
X sin A – y cos A = n, then prove that: x2 + y2 = m2 + n2

Exercise 21(B) | Q 3 | Page 327

If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 - n2 = a2 - b2

Exercise 21(B) | Q 4 | Page 327

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that: x2 + y2 + z2 = r2

Exercise 21(B) | Q 5 | Page 327

If sin A + cos A = m and sec A + cosec A = n, show that: n (m2 - 1) = 2m

Exercise 21(B) | Q 6 | Page 327

If x = r cos A cos B, y = r cos A sin B and Z = r sin A, show that:
x2 + y2 + z2 = r2

Exercise 21(B) | Q 7 | Page 327

If `cosA/cosB=m` and `cosA/sinB` = n show that:

`(m^2+n^2)cos^2B=n^2`.

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise Exercise 21(C) [Pages 328 - 329]

Exercise 21(C) | Q 1.1 | Page 328

Show that:
tan10° tan15° tan75° tan80° = 1

Exercise 21(C) | Q 1.2 | Page 328

Show that:
sin 42° sec 48° + cos 42° cos ec48° = 2

Exercise 21(C) | Q 1.3 | Page 328

Show that:
`sin26^@/sec64^@+cos26^@/(cosec64^@)=1`

Exercise 21(C) | Q 2.1 | Page 328

Express the following in terms of angles between 0° and 45°:

sin59° + tan63°

Exercise 21(C) | Q 2.2 | Page 328

Express the following in terms of angles between 0° and 45°:

cosec68° + cot72°

Exercise 21(C) | Q 2.3 | Page 328

Express the following in terms of angles between 0° and 45°:

cos74° + sec67°

Exercise 21(C) | Q 3.1 | Page 328

Show that:

`sinA/sin(90^@-A)+cosA/cos(90^@-A)=secA cosecA`

Exercise 21(C) | Q 3.2 | Page 328

Show that:

`sinAcosA-(sinAcos(90^@-A)cosA)/sec(90^@-A)-(cosAsin(90^@-A)sinA)/(cosec(90^@-A))=0`

Exercise 21(C) | Q 4.1 | Page 328

For triangle ABC, show that:

`sin (A+B)/2=cosC/2`

Exercise 21(C) | Q 4.2 | Page 328

For triangle ABC, show that:

`tan  (B+C)/2=cot  A/2`

Exercise 21(C) | Q 5.1 | Page 328

Evaluate:

`3 sin72^@/(cos18^@)-sec32^@/(cosec58^@)`

Exercise 21(C) | Q 5.2 | Page 328

Evaluate:

3cos80° cosec10° + 2 cos59° cosec31°

 

Exercise 21(C) | Q 5.3 | Page 328

Evaluate:

`sin80^@/(cos10^@)+sin59^@ sec31^@`

Exercise 21(C) | Q 5.4 | Page 328

Prove that:

tan(55° + A) = cot(35° - A)

Exercise 21(C) | Q 5.5 | Page 328

Evaluate:

cosec(65° + A) - sec(25° - A)

Exercise 21(C) | Q 5.6 | Page 328

Evaluate:

`2 tan57^@/(cot33^@)-cot70^@/(tan20^@)-sqrt2 cos45^@`

Exercise 21(C) | Q 5.7 | Page 328

Evaluate:

`(cot^2 41^@)/(tan^2 49^@)-2 sin^2 75^@/cos^2 15^@`

Exercise 21(C) | Q 5.8 | Page 328

Evaluate:

`cos70^@/(sin20^@)+cos59^@/(sin31^@)-8 sin^2 30^@`

Exercise 21(C) | Q 5.9 | Page 328

Evaluate:

14 sin30° + 6 cos60° - 5 tan45°

Exercise 21(C) | Q 6 | Page 329

A triangle ABC is right angles at B; find the value of`(secAcosecA-tanAcotC)/sinB`

Exercise 21(C) | Q 7.1 | Page 329

Find the value of x, if sin x = sin60° cos30° - cos60° sin30°

Exercise 21(C) | Q 7.2 | Page 329

Find the value of x, if sin x = sin60° cos30° + cos60° sin30°

Exercise 21(C) | Q 7.3 | Page 329

Find the value of x, if cos x = cos60° cos30° - sin60° sin30°

Exercise 21(C) | Q 7.4 | Page 329

Find the value of x, if  tan x`=(tan60^@-tan30^@)/(1+tan60^@tan30^@)`

Exercise 21(C) | Q 7.5 | Page 329

Find the value of x, if sin2x = 2sin 45° cos 45°

Exercise 21(C) | Q 7.6 | Page 329

Find the value of x, if sin3x = 2sin 30° cos30°

Exercise 21(C) | Q 7.7 | Page 329

Find the value of x, if cos(2x - 6) = cos230° - cos260°

Exercise 21(C) | Q 8.1 | Page 329

find the value of angle A, where 0° ≤ A ≤ 90°.

sin(90° - 3A).cosec42° = 1

Exercise 21(C) | Q 8.2 | Page 329

find the value of angle A, where 0° ≤ A ≤ 90°.

cos(90° - A).sec 77° = 1

Exercise 21(C) | Q 9.1 | Page 329

Prove that:

`(cos(90^@-theta)costheta)/cottheta=1-cos^2theta`

Exercise 21(C) | Q 9.2 | Page 329

Prove that:

`(sinthetasin(90^@-theta))/cot(90^@-theta)=1-sin^2theta`

Exercise 21(C) | Q 10 | Page 329

Evaluate:

`(sin35^@cos55^@+cos35^@sin55^@)/(cosec^2 10^@-tan^2 80^@)`

Exercise 21(C) | Q 11 | Page 329

Evaluate

sin2 34° + sin56° + 2tan 18° tan72° - cot30°

Exercise 21(C) | Q 12 | Page 329

Without using trigonometrical tables, evaluate:

`cosec^2 57^@ - tan^2 33^@ + cos 44^@ cosec 46^@ - sqrt2 cos 45^@ -  tan^2 60^@`

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise Exercise 21(D) [Page 331]

Exercise 21(D) | Q 1.1 | Page 331

Use tables to find sine of 21°

Exercise 21(D) | Q 1.2 | Page 331

Use tables to find sine of 34° 42'

Exercise 21(D) | Q 1.3 | Page 331

Use tables to find sine of 47° 32'

Exercise 21(D) | Q 1.4 | Page 331

Use tables to find sine of 62° 57'

Exercise 21(D) | Q 1.5 | Page 331

Use tables to find sine of 10° 20' + 20° 45'

Exercise 21(D) | Q 2.1 | Page 331

Use tables to find cosine of 2° 4’

Exercise 21(D) | Q 2.2 | Page 331

Use tables to find cosine of 8° 12’

Exercise 21(D) | Q 2.3 | Page 331

Use tables to find cosine of 26° 32’

Exercise 21(D) | Q 2.4 | Page 331

Use tables to find cosine of 65° 41’

Exercise 21(D) | Q 2.5 | Page 331

Use tables to find cosine of 9° 23’ + 15° 54’

Exercise 21(D) | Q 3.1 | Page 331

Use trigonometrical tables to find tangent of 37°

Exercise 21(D) | Q 3.2 | Page 331

Use trigonometrical tables to find tangent of 42° 18'

Exercise 21(D) | Q 3.3 | Page 331

Use trigonometrical tables to find tangent of 17° 27'

Exercise 21(D) | Q 4.1 | Page 331

Use tables to find the acute angle θ, if the value of sin θ is 0.4848

Exercise 21(D) | Q 4.2 | Page 331

Use tables to find the acute angle θ, if the value of sin θ is 0.3827

Exercise 21(D) | Q 4.3 | Page 331

Use tables to find the acute angle θ, if the value of sin θ is 0.6525

Exercise 21(D) | Q 5.1 | Page 331

Use tables to find the acute angle θ, if the value of cos θ is 0.9848

Exercise 21(D) | Q 5.2 | Page 331

Use tables to find the acute angle θ, if the value of cos θ is 0.9574

Exercise 21(D) | Q 5.3 | Page 331

Use tables to find the acute angle θ, if the value of cos θ is 0.6885

Exercise 21(D) | Q 6.1 | Page 331

Use tables to find the acute angle θ, if the value of tan θ is 0.2419

Exercise 21(D) | Q 6.2 | Page 331

Use tables to find the acute angle θ, if the value of tan θ is 0.4741

Exercise 21(D) | Q 6.3 | Page 331

Use tables to find the acute angle θ, if the value of tan θ is 0.7391

Selina solutions for Concise Mathematics Class 10 ICSE Chapter 21 Trigonometrical Identities Exercise Exercise 21(E) [Pages 332 - 333]

Exercise 21(E) | Q 1.01 | Page 332

Prove the following identitie:

`1/(cosA+sinA)+1/(cosA-sinA)=(2cosA)/(2cos^2A-1)`

Exercise 21(E) | Q 1.02 | Page 332

Prove the following identitie:

`cosecA-cotA=sinA/(1+cosA`

 

Exercise 21(E) | Q 1.03 | Page 332

Prove the following identitie:

`1-sin^2A/(1+cosA)=cosA`

Exercise 21(E) | Q 1.04 | Page 332

Prove the following identitie:

`(1-cosA)/sinA+sinA/(1-cosA)=2 cosecA`

Exercise 21(E) | Q 1.05 | Page 332

Prove the following identitie:

`cotA/(1-tanA)+tanA/(1-cotA)=1+tanA+cotA`

 

Exercise 21(E) | Q 1.06 | Page 332

Prove the following identitie:

`cosA/(1+sinA)+tanA=secA`

Exercise 21(E) | Q 1.07 | Page 332

Prove the following identitie:

`sinA/(1-cosA)-cotA=cosecA`

Exercise 21(E) | Q 1.08 | Page 332

Prove the following identitie:

`(sinA-cosA+1)/(sinA+cosA-1)=cosA/(1-sinA)`

Exercise 21(E) | Q 1.09 | Page 332

Prove the following identitie:

`sqrt((1+sinA)/(1-sinA))=cosA/(1-sinA)`

Exercise 21(E) | Q 1.1 | Page 332

Prove the following identitie:

`sqrt((1-cosA)/(1+cosA))=sinA/(1+cosA)`

Exercise 21(E) | Q 1.11 | Page 332

Prove the following identitie:

`(1+(secA-tanA)^2)/(cosecA(secA-tanA))=2tanA`

Exercise 21(E) | Q 1.12 | Page 332

Prove the following identitie:

`((cosecA-cotA)^2+1)/(secA(cosecA-cotA))=2cotA`

Exercise 21(E) | Q 1.13 | Page 332

Prove the following identitie:

`cot^2A((secA-1)/(1+sinA))+sec^2A((sinA-1)/(1+secA))=0`

Exercise 21(E) | Q 1.14 | Page 332

Prove the following identitie:

`(1-2sin^2A)^2/(cos^4A-sin^4A)=2cos^2A-1`

Exercise 21(E) | Q 1.15 | Page 332

Prove the following identitie:

sec4A (1 - sin4A) - 2 tan2A = 1

Exercise 21(E) | Q 1.16 | Page 332

Prove the following identitie:

cosec4A (1 - cos4A) - 2 cot2A = 1

Exercise 21(E) | Q 1.17 | Page 332

Prove the following identitie:

(1 + tanA + secA)(1 + cotA - cosecA) = 2

Exercise 21(E) | Q 2 | Page 332

If sinA + cosA = p

 and secA + cosecA = q, then prove that: q(p2 - 1) = 2p

Exercise 21(E) | Q 3 | Page 332

If x = a cosθ and y = b cotθ, show that:

`a^2/x^2-b^2/y^2=1` 

Exercise 21(E) | Q 4 | Page 332

If secA + tanA = p, show taht:

sinA = `(p^2-1)/(p^2+1)`

Exercise 21(E) | Q 5 | Page 332

If tanA = n tanB and sinA = m sinB, prove that:

`cos^2A=(m^2-1)/(n^2-1)`

Exercise 21(E) | Q 6.1 | Page 332

If 2 sin A – 1 = 0, show that: Sin 3A = 3 sin A – 4 sin3A

Exercise 21(E) | Q 6.2 | Page 332

If 4 cos2 A – 3 = 0, Show that:
cos 3 A = 4 cos3 A – 3 cos A

Exercise 21(E) | Q 7.1 | Page 332

Evaluate

`2(tan35^@/cot55^@)+(cot55^@/tan35^@)-3(sec40^@/(cosec50^@))`

Exercise 21(E) | Q 7.2 | Page 332

Evaluate

`sec26^@ sin64^@+(cosec33^@)/sec57^@`

Exercise 21(E) | Q 7.3 | Page 332

Evaluate

`(5sin66^@)/(cos24^@)-(2cot85^@)/tan5^@` 

Exercise 21(E) | Q 7.4 | Page 332

Evaluate

cos40° cosec50° + sin50° sec40°

Exercise 21(E) | Q 7.5 | Page 332

Evaluate

sin27° sin63° - cos63° cos27°

Exercise 21(E) | Q 7.6 | Page 332

Evaluate

`(3sin72^@)/(cos18^@)-sec32^@/(cosec58^@)`

Exercise 21(E) | Q 7.7 | Page 332

Evaluate

3 cos80° cosec10°+ 2 cos59° cosec31°

Exercise 21(E) | Q 7.8 | Page 332

Evaluate

`cos75^@/(sin15^@)+sin12^@/(cos78^@)-cos18^@/sin72^@`

Exercise 21(E) | Q 8.1 | Page 332

Prove that: tan (55° + x) = cot (35° - x)

Exercise 21(E) | Q 8.2 | Page 332

Prove that:

sec(70° - θ) = cosec(20° + θ)

Exercise 21(E) | Q 8.3 | Page 332

Prove that:

sin(28° + A) = cos(62° - A)

Exercise 21(E) | Q 8.4 | Page 332

Prove that:

`1/(1+cos(90^@ - A))+ 1/(1-cos(90^@-A))=2cosec^2(90^@-A)`

Exercise 21(E) | Q 8.5 | Page 332

Prove that:

`1/(1+sin(90^@-A))+1/(1-sin(90^@-A))=2sec^2(90^@-A)`

Exercise 21(E) | Q 9.1 | Page 332

If A and B are complementary angles, prove that:

cotB + cosB = secA cosB (1 + sinB)

 

Exercise 21(E) | Q 9.2 | Page 332

If A and B are complementary angles, prove that:

cotA cotB - sinA cosB  - cosA sinB = 0

 

Exercise 21(E) | Q 9.3 | Page 332

If A and B are complementary angles, prove that:

cosec2A + cosec2B = cosec2A cosec2B

 

Exercise 21(E) | Q 9.4 | Page 332

If A and B are complementary angles, prove that:

`(sinA+sinB)/(sinA-sinB)+(cosB-cosA)/(cosB+cosA)=2/(2sin^2A-1)`

 

Exercise 21(E) | Q 10.01 | Page 333

Prove that

`1/(sinA-cosA)-1/(sinA+cosA)=(2cosA)/(2sin^2A-1)`

Exercise 21(E) | Q 10.02 | Page 333

Prove that

`cot^2A/(cosecA-1)-1=cosecA`

Exercise 21(E) | Q 10.03 | Page 333

Prove that

`cosA/(1+sinA)=secA-tanA`

Exercise 21(E) | Q 10.04 | Page 333

Prove that

cosA (1 + cotA) + sinA (1 + tanA = secA + cosecA

Exercise 21(E) | Q 10.05 | Page 333

Prove that

`(sinA-cosA)(1+tanA+cotA)=secA/(cosec^2A)-(cosecA)/sec^2A`

Exercise 21(E) | Q 10.06 | Page 333

Prove that

`sqrt(sec^2A+cosec^2A)=tanA + cotA`

Exercise 21(E) | Q 10.07 | Page 333

Prove that

(sinA + cosA) (secA + cosecA) = 2 + secA cosecA

Exercise 21(E) | Q 10.08 | Page 333

Prove that

(tanA + cotA) (cosecA - sinA) (secA - cosA) = 1

Exercise 21(E) | Q 10.09 | Page 333

Prove that

`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`

Exercise 21(E) | Q 10.1 | Page 333

Prove that: `("cot A" - 1)/(2 - "sec"^2 "A") = "cot A"/(1 + "tan  A")` 

Exercise 21(E) | Q 11.1 | Page 333

If 4 cos2 A – 3 = 0 and ≤ A ≤ 90°, then prove that :
sin 3 A = 3 sin A – 4 sin3 A

Exercise 21(E) | Q 11.2 | Page 333

If 4 cos2 A – 3 = 0 and ≤ A ≤ 90°, then prove that:
cos 3 A = 4 cos3 A – 3 cos A

Exercise 21(E) | Q 12.1 | Page 333

Find A, if 0° ≤ A ≤ 90° and 2cos2A - 1 = 0

Exercise 21(E) | Q 12.2 | Page 333

Find A, if 0° ≤ A ≤ 90° and sin 3A - 1 = 0

Exercise 21(E) | Q 12.3 | Page 333

Find A, if 0° ≤ A ≤ 90° and 4sin2A - 3 = 0

Exercise 21(E) | Q 12.4 | Page 333

Find A, if 0° ≤ A ≤ 90° and cos2A - cosA = 0

Exercise 21(E) | Q 12.5 | Page 333

Find A, if 0° ≤ A ≤ 90° and 2cos2A + cosA - 1 = 0

Exercise 21(E) | Q 13.1 | Page 333

If 0° < A < 90°; Find A, if :

`(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4` 

Exercise 21(E) | Q 13.2 | Page 333

If 0° < A < 90°; Find A, if `sinA/(secA-1)+sinA/(secA+1)=2`

Exercise 21(E) | Q 14 | Page 333

Prove that:

(cosecA - sinA) (secA - cosA) sec2A = tanA

Exercise 21(E) | Q 15 | Page 333

Prove the identity (sin θ + cos θ) (tan θ + cot θ ) = sec θ + cosec θ

Exercise 21(E) | Q 16 | Page 333

Evaluate without using trigonometric tables, 

`sin^2 28^@ + sin^2 62^@ + tan^2 38^@ - cot^2 52^@ + 1/4 sec^2 30^@`

Chapter 21: Trigonometrical Identities

Exercise 21(A)Exercise 21(B)Exercise 21(C)Exercise 21(D)Exercise 21(E)
Concise Mathematics Class 10 ICSE - Shaalaa.com

Selina solutions for Concise Mathematics Class 10 ICSE chapter 21 - Trigonometrical Identities

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 21 Trigonometrical Identities are Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables, Trigonometry Problems and Solutions.

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