Simplify: cos2θ1−tanθ+sin3θsinθ−cosθ
Answer:
1+sinθ cosθ
- cos2θ1−tanθ+sin3θsinθ−cosθ=cosθcos2θcosθ−cosθtanθ+sin3θsinθ−cosθ[Multiply numerator and denominator of first term by cosθ]=cos3θcosθ−sinθ−sin3θcosθ−sinθ=cos3θ−sin3θcosθ−sinθ=(cosθ−sinθ)(cos2θ+sin2θ+sinθcosθ)cosθ−sinθ [Since, x3−y3=(x+y)(x2+y2+xy)]=1+sinθ cosθ [Since, sin2θ+cos2θ=1]