Let theta = x for typing purposes here.

We will the formula of because (2x) = 2 ( because x)^2 - 1cos (4x) = because [2 * (2x)]. Let 2x = y.

Now using the formula

because (2y) = 2 ( because y)^2 - 1 = 2 [because (2x)]^2 - 1

Therefore

because (2y) = because (4x) = 2 [because (2x)]^2 - 1

We will the formula of because (2x) = 2 ( because x)^2 - 1cos (4x) = because [2 * (2x)]. Let 2x = y.

Now using the formula

because (2y) = 2 ( because y)^2 - 1 = 2 [because (2x)]^2 - 1

Therefore

because (2y) = because (4x) = 2 [because (2x)]^2 - 1