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For sinθ ≠ cosθ, the expression (co $s^{3}$ θ − si $n^{3}$ θ)/(cosθ − sinθ) simplifies to:

Competition practiceTrigonometry

A1 − sinθ·cosθ
Bsinθ·cosθ
C1 + sinθ·cosθ
D1 + 2sinθ·cosθ

Step-by-Step Solution

Use

a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2})

. Cancelling (cosθ − sinθ) leaves co

s^{2}

θ + sinθ·cosθ + si

n^{2}

θ = 1 + sinθ·cosθ.

Answer: C) 1 + sinθ·cosθ

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