Solve the trigonometric equation .

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

Problem

Solve the trigonometric equation 2sin⁡2x−3sin⁡x+1=02\sin^{2}x - 3\sin x + 1 = 0. (a) Obtain the general solution of the equation. (b) How many solutions of the equation obtained in part (a) lie in the interval [−π2, 3π2]\left[-\dfrac{\pi}{2},\,\dfrac{3\pi}{2}\right]? List all such solutions with justification.

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