Question

Express cos 2A in terms of Sin A divided by 2​

Answer 1

Answer:

Now, putting B = A on both sides of the above formula we get,

cos (A + A) = cos A cos A - sin A sin A

⇒ cos 2A = cos2 A - sin2 A

⇒ cos 2A = cos2 A - (1 - cos2 A), [since we know that sin2 θ = 1 - cos2 θ]

⇒ cos 2A = cos2 A - 1 + cos2 A,

⇒ cos 2A = 2 cos2 A - 1

⇒ cos 2A = 2 (1 - sin2 A) - 1, [since we know that cos2 θ = 1 - sin2 θ]

⇒ cos 2A = 2 - 2 sin2 A - 1

⇒ cos 2A = 1 - 2 sin2 A