If cos A + cos 2 A = 1, then sin 2 A + sin 4 A

Question

Philoid · Accepted Answer

Given: cos A + cos² A = 1

⇒ cos A = 1 – cos² A = sin² A [∵ sin² A + cos² A = 1]……(i)

Squaring both sides, we get

⇒ cos² A = (sin² A)² = sin⁴ A ……(ii)

To find: sin² A + sin⁴ A

Consider sin² A + sin⁴ A = cos A + cos² A [From (i) and (ii)]

= 1