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Sin + sin 2 / 1+cos + cos 2​

Answer»

Question

sinθ + sin²θ/1 + cosθ + cos2θ = tanθ

Explanation:

SIN(2θ) = 2sinθcos θ

cos(2θ) = 2cos2θ − 1

tanθ = sinθcosθ

Therefore,

LHS = (sinθ+sin2θ/(1+cosθ+cos2θ)

= (sinθ+2sinθcosθ)/(1+cosθ+2cos2θ−1)

= sinθ(1+2cosθ) / cosθ(1+2cosθ)

= tanθ

= RHS



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