Simplify: 1sin3θ+cos3θsinθ+cosθ


Answer:

sinθ cosθ

Step by Step Explanation:
  1. 1sin3θ+cos3θsinθ+cosθ = 1(sinθ+cosθ)(sin2θ+cos2θsinθcosθ)sinθ+cosθ   [x3+y3=(x+y)(x2+y2xy)]
  2. Now, sinθ+cosθ cancels out.
    1(sin2θ+cos2θsinθcosθ)1(1sinθcosθ)  [sin2θ+cos2θ=1]11+sinθcosθsinθ+cosθ

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