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Frank solutions for Class 10 Maths chapter 21 - Trigonometric Identities

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Frank Frank Class 10 Mathematics Part 2

Frank Class 10 Mathematics Part 2 - Shaalaa.com

Chapter 21: Trigonometric Identities

Exercise 21.1Exercise 21.2Exercise 21.3

Frank solutions for Class 10 Maths Chapter 21 Exercise Exercise 21.1 [Page 0]

Prove the following identity :

`(1 - sin^2θ)sec^2θ = 1`

Prove the following identity :

`(1 - cos^2θ)sec^2θ = tan^2θ`

Prove the following identity :

tanA+cotA=secAcosecA 

Prove the following identity :

`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ` 

Prove the following identity :

 ( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ) 

Prove the following identity :

sinθcotθ + sinθcosecθ = 1 + cosθ  

Prove the following identity :

secA(1 - sinA)(secA + tanA) = 1

Prove the following identity :

secA(1 + sinA)(secA - tanA) = 1

Prove the following identity :

cosecθ(1 + cosθ)(cosecθ - cotθ) = 1

Prove the following identity : 

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

Prove the following identity :

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

Prove the following identity :

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

Prove the following identity :

`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`

Prove the following identity : 

`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`

Prove the following identity :

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

Prove the following identity :

`cosec^4A - cosec^2A = cot^4A + cot^2A`

Prove the following identity :

`sec^2A + cosec^2A = sec^2Acosec^2A`

Prove the following identity :

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

Prove the following identity :

`tan^2A - sin^2A = tan^2A.sin^2A`

Prove the following identity :

(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`

Prove the following identity :

`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`

Prove the following identity :

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

Prove the following identity :

`sec^2A.cosec^2A = tan^2A + cot^2A + 2`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`

Prove the following Identities :

`(cosecA)/(cotA+tanA)=cosA`

Prove the following identities:

`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`

Prove the following identities:

`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`

Prove the following identity : 

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

Prove the following identity :

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

Prove the following identity :

`(cotA + tanB)/(cotB + tanA) = cotAtanB`

Prove the following identity :

`1/(tanA + cotA) = sinAcosA`

Prove the following identity :

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`sqrt(cosec^2q - 1) = "cosq  cosecq"`

Prove the following identity : 

`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq

Prove the following identity : 

`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`

Prove the following identity : 

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity :

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

Prove the following identity  :

`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`

Prove the following identity : 

`(cosecθ)/(tanθ + cotθ) = cosθ`

Prove the following identity : 

`(1 + tan^2θ)sinθcosθ = tanθ`

Prove the following identity : 

`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`

Prove the following identity : 

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

Prove the following identity : 

`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`

Prove the following identity : 

`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`

Prove the following identity : 

`sec^4A - sec^2A = sin^2A/cos^4A`

Prove the following identity :

`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`

Prove the following identity :

`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`

Prove the following identity :

`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`

Prove the following identity :

`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`

Prove the following identity : 

`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`

Prove the following identity :

`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`

Frank solutions for Class 10 Maths Chapter 21 Exercise Exercise 21.2 [Page 0]

If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2

If `x/(a cosθ) = y/(b sinθ)   "and"  (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that"  x^2/a^2 + y^2/b^2 = 1`

If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that   `x^2 + y^2 + z^2 = r^2`

If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m

If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`

If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1

If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`

If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn 

If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`

If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)

Frank solutions for Class 10 Maths Chapter 21 Exercise Exercise 21.3 [Page 0]

Without using trigonometric table , evaluate : 

`cosec49°cos41° + (tan31°)/(cot59°)`

Without using trigonometric table , evaluate : 

`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`

Without using trigonometric table , evaluate : 

`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`

Without using trigonometric table , evaluate : 

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`

Without using trigonometric table , evaluate : 

`sin72^circ/cos18^circ  - sec32^circ/(cosec58^circ)`

Find the value of `θ(0^circ < θ < 90^circ)` if : 

`cos 63^circ sec(90^circ - θ) = 1`

Find the value of `θ(0^circ < θ < 90^circ)` if : 

`tan35^circ cot(90^circ - θ) = 1`

Without using trigonometric identity , show that :

`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`

Without using trigonometric identity , show that :

`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`

Without using trigonometric identity , show that :

`sin(50^circ + θ) - cos(40^circ - θ) = 0`

Without using trigonometric identity , show that :

`cos^2 25^circ + cos^2 65^circ = 1`

Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`

Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`

For ΔABC , prove that : 

`tan ((B + C)/2) = cot "A/2`

For ΔABC , prove that : 

`sin((A + B)/2) = cos"C/2`

Prove that  `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`

Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`

Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`

Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A

prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`

Chapter 21: Trigonometric Identities

Exercise 21.1Exercise 21.2Exercise 21.3

Frank Frank Class 10 Mathematics Part 2

Frank Class 10 Mathematics Part 2 - Shaalaa.com

Frank solutions for Class 10 Mathematics chapter 21 - Trigonometric Identities

Frank solutions for Class 10 Maths chapter 21 (Trigonometric 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 Frank Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10 Mathematics chapter 21 Trigonometric 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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