Question

Prove cos(2x) = cos²x-sin²x​

Answer 1

We can write

cos 2x = cos(x+x) = cos x cos x - sin x

sin x = cos²x - sin²x.

Using the trigonometric identity sin²x + cos²x = 1,

we get

sin²x = 1 - cos²x and cos²x = 1 - sin²x.

Therefore cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x.

Answer 2

Answer:

Step-by-step explanation:

We will use the angle-sum identity for cosine

cos(α+β) = cosα * cosβ - sinα * sinβ

==> cos(x + x) = cos x * cos x - sin x * sin x

thus cos(2x) = $cos^{2}$ x - $sin^{2}$ x