If sin x = cos 2 x, then write the value of cos 2 x (1 + cos 2 x).

Question

Philoid · Accepted Answer

Given sin x = cos²x

To find the value of cos² x (1 + cos² x).

⇒ cos² x (1 + cos² x).

⇒ cos² x + cos⁴ x.

As cos²x = 1- sin²x the above equation becomes

⇒ 1- sin²x + sin²x

⇒ 1.

If sin x = cos2 x, then write the value of cos2 x (1 + cos2 x).