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Selina solutions for Class 10 Mathematics chapter 21 - Trigonometrical Identities

Selina ICSE Concise Mathematics for Class 10

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Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10

Chapter 21 : Trigonometrical Identities

Page 0

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

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

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

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

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

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

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

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

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

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

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

Prove.
tan2A - sin2A = tan2A sin2A

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

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

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

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

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

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

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

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

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

prove.
sec2A cosec2A = tan2A + cot2A + 2

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

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

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

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

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

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

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

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

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

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

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

 

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

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

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

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

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

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

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

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

 

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

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

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

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

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

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

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

Page 0

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

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

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

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

Prove.
 2 sin2A + cos4A = 1 + sin4

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

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

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

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

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

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

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

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

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

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

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

Page 0

Solve.
`cos22/sin68`

Solve.
`tan47/cot43`

Solve.
`sec75/(cosec15)`

Solve.
`cos55/sin35+cot35/tan55`

solve.
cos240° + cos250°

solve.
sec18° - cot2 72°

Solve.
sin15° cos75° + cos15° sin75°

Solve.
sin42° sin48° - cos42° cos48°

Evaluate.
sin(90° - A) cosA + cos(90° - A) sinA

Evaluate.
sin235° + sin255°

Evaluate.
`cot54^@/(tan36^@)+tan20^@/(cot70^@)-2`

Evaluate.
`(2tan53^@)/(cot37^@)-cot80^@/tan10^@`

Evaluate.
cos225° + cos265° - tan245°

Evaluate.
`(cos^2 32^@+cos^2 58^@)/(sin^2 59^@+sin^2 31^@)`

Evaluate.
`(sin77^@/cos13^@)^2+(cos77^@/sin13^@)-2cos^2 45^@`

Evaluate.
`cos^2 26^@+cos65^@sin26^@+tan36^@/cot54^@`

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

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

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

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

sin59° + tan63°

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

cosec68° + cot72°

 

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

cos74° + sec67°

Show that:

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

Show that:

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

For triangle ABC, show that:

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

For triangle ABC, show that:

`tan  (B+C)/2=cot  A/2`

Evaluate:

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

Evaluate:

3cos80° cosec10° + 2 cos59° cosec31°

 

Evaluate:

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

Evaluate:

tan(55° - A) - cot(35° + A)

Evaluate:

cosec(65° + A) - sec(25° - A)

Evaluate:

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

Evaluate:

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

Evaluate:

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

Evaluate:

14 sin30° + 6 cos60° - 5 tan45°

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

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

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

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

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

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

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

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

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

sin(90° - 3A).cosec42° = 1

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

cos(90° - A).sec 77° = 1

Prove that:

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

Prove that:

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

Evaluate:

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

Page 0

Use tables to find sine of 21°

Use tables to find sine of 34° 42'

Use tables to find sine of 47° 32'

Use tables to find sine of 62° 57'

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

Use tables to find cosine of 2° 4’

Use tables to find cosine of 8° 12’

Use tables to find cosine of 26° 32’

Use tables to find cosine of 65° 41’

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

Use trigonometrical tables to find tangent of 37°

Use trigonometrical tables to find tangent of 42° 18'

Use trigonometrical tables to find tangent of 17° 27'

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

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

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

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

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

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

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

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

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

Page 0

Prove the following identitie:

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

Prove the following identitie:

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

 

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

 

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

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

Prove the following identitie:

sec4A (1 - sin4A) - 2 tan2A = 1

Prove the following identitie:

cosec4A (1 - cos4A) - 2 cot2A = 1

Prove the following identitie:

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

If sinA + cosA = p

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

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

`a^2/x^2-b^2/y^2=1` 

If secA + tanA = p, show taht:

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

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

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

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

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

Evaluate

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

Evaluate

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

Evaluate

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

Evaluate

cos40° cosec50° + sin50° sec40°

Evaluate

sin27° sin63° - cos63° cos27°

Evaluate

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

Evaluate

3 cos80° cosec10°+ 2 cos59° cosec31°

Evaluate

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

Prove that:

tan(55° + x) = cot(35° - x)

Prove that:

sec(70° - θ) = cosec(20° + θ)

Prove that:

sin(28° + A) = cos(62° - A)

Prove that:

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

Prove that:

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

If A and B are complementary angles, prove that:

cotB + cosB = secA cosB (1 + sinB)

 

If A and B are complementary angles, prove that:

cotA cotB - sinA cosB  - cosA sinB = 0

 

If A and B are complementary angles, prove that:

cosec2A + cosec2B = cosec2A cosec2B

 

If A and B are complementary angles, prove that:

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

 

Prove that

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

Prove that

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

Prove that

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

Prove that

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

Prove that

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

Prove that

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

Prove that

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

Prove that

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

Prove that

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

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

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

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

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

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

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

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

If 0° < A < 90°; Find A, if :

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

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

Prove that:

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

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10

Selina solutions for Class 10 Mathematics chapter 21 - Trigonometrical Identities

Selina solutions for Class 10 Maths chapter 21 (Trigonometrical Identities) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics 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.

Using Selina Class 10 solutions Trigonometrical Identities exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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