Simplify: cos2θ1tanθ+sin3θsinθcosθ


Answer:

1+sinθ cosθ

Step by Step Explanation:
  1. cos2θ1tanθ+sin3θsinθcosθ=cosθcos2θcosθcosθtanθ+sin3θsinθcosθ[Multiply numerator and denominator of first term by cosθ]=cos3θcosθsinθsin3θcosθsinθ=cos3θsin3θcosθsinθ=(cosθsinθ)(cos2θ+sin2θ+sinθcosθ)cosθsinθ [Since, x3y3=(x+y)(x2+y2+xy)]=1+sinθ cosθ [Since, sin2θ+cos2θ=1]

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