Simplify: 1sin3θ+cos3θsinθ+cosθ


Answer:

sinθ cosθ

Step by Step Explanation:
  1. 1sin3θ+cos3θsinθ+cosθ = 1(sinθ+cosθ)(sin2θ+cos2θsinθcosθ)sinθ+cosθ   [
  2. Now, sin \theta + cos \theta cancels out.
    \begin{align} &1 - (sin^2 \theta + cos^2 \theta - sin \theta cos \theta) \\ &\implies 1 - (1 - sin \theta cos \theta) \space \space [\because sin^2 \theta + cos^2 \theta = 1] \\ &\implies 1 - 1 + sin \theta cos \theta \\ &\implies sin \theta + cos \theta \end{align}

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