 ## Book: RD Sharma - Mathematics (Volume 1)

### Chapter: 4. Inverse Trigonometric Functions

#### Subject: Maths - Class 12th

##### Q. No. 13 of MCQ

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13
##### Choose the correct answerIf , then We are given with, …(i)

We need to find the value of Take Left Hand Side (LHS) of equation (i),

Using the property of inverse trigonometry, Putting and ,    Equate LHS to RHS. Taking cosine on both sides, Using property of inverse trigonometry,

cos(cos-1 A) = A Simplifying the equation,    Squaring on both sides, Using algebraic identity,

(A – B)2 = A2 + B2 – 2AB    Using trigonometric identity,

cos 2θ = cos2 θ – sin2 θ …(ii)

sin2 θ + cos2 θ = 1 sin2 θ = 1 – cos2 θ …(iii)

Putting value of sin2 θ from equation (iii) in equation (ii), we get

cos 2θ = cos2 θ – (1 – cos2 θ)

Or, cos 2θ = cos2 θ – 1 + cos2 θ

Or, cos 2θ = 2 cos2 θ – 1

Or, 2 cos2 θ = cos 2θ + 1

Replace θ by θ/2.  Substituting the value of in     1

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