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