Question

value of cos4a and its formula​

Answer 1

Answer:

How to proof the formula of cos 2A is equals cos A - sin A?

Or

How to proof the formula of cos 2A is equals 1 - 2 sin A?

Or

How to proof the formula of cos 2A is equals 2 cos A - 1?

We know that for two real numbers or angles A and B,

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

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 = cos A - sin A

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

⇒ cos 2A = cos A - 1 + cos A,

⇒ cos 2A = 2 cos A - 1

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

⇒ cos 2A = 2 - 2 sin A - 1

⇒ cos 2A = 1 - 2 sin A