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

Question

Philoid · Accepted Answer

Given: sin θ + sin² θ = 1

⇒ sin θ = 1 – sin² θ = cos² θ [∵ sin² θ + cos² θ = 1]……(i)

⇒ Sin² θ = (cos² θ)² = cos⁴ θ ……(ii)

To find: cos² θ + cos⁴ θ

Consider cos² θ + cos⁴ θ = sin θ + sin² θ [Using (i) and (ii)]

= 1 [Given]