RD Sharma - Mathematics (Volume 1)

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 answer

If , 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






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