Q8 of 80 Page 311

If sin θ + sin2 θ = 1, then let us prove that, cos2 θ + cos4 θ = 1.

Given, sinθ + sin2θ = 1


⇒ sinθ + sin2θ = sin2θ + cos2θ


⇒ sinθ = cos2θ


⇒ squaring on both sides


⇒ (sinθ)2 = (cos2θ)2


⇒ sin2θ = cos4θ


⇒ sinθ + sin2θ = 1


⇒ cos2θ + cos4θ = 1


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