Simplify: 1−sin3θ+cos3θsinθ+cosθ
Answer:
sinθ cosθ
- 1−sin3θ+cos3θsinθ+cosθ = 1−(sinθ+cosθ)(sin2θ+cos2θ−sinθcosθ)sinθ+cosθ [∵
- 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}