Solve the equation .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the equation sin⁡(2θ−π)=sin⁡(θ+π3)\sin\bigl(2\theta-\pi\bigr)=\sin\bigl(\theta+\tfrac{\pi}{3}\bigr). (i) Derive the general solution for θ\theta. (ii) Hence find all values of θ\theta in the interval 0≤θ<2π0 \le \theta < 2\pi that satisfy the equation.

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