Simplify: 1−sin3θ+cos3θsinθ+cosθ
Answer:
sinθ cosθ
- 1−sin3θ+cos3θsinθ+cosθ = 1−(sinθ+cosθ)(sin2θ+cos2θ−sinθcosθ)sinθ+cosθ [∵x3+y3=(x+y)(x2+y2−xy)]
- Now, sinθ+cosθ cancels out.
1−(sin2θ+cos2θ−sinθcosθ)⟹1−(1−sinθcosθ) [∵sin2θ+cos2θ=1]⟹1−1+sinθcosθ⟹sinθ+cosθ