Question

If sin theta+ sin^2 theta=1 prove that cos^2 theta + cos^4 =1​

Answer 1

sin a + sin²a = 1-----------------i

» sin a = 1- sin² a (since cos² a = 1- sin ² a)

» sin a = cos ² a----------------ii

substituting the value of sin a in eq 1

(cos² a ) + (cos² a) ² = 1

» cos ² a + cos ⁴ a = 1

hence proved