Solve the equation and answer the following.

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

Problem

Solve the equation 2sin⁡x cos⁡x (1−2sin⁡2x)=02\sin x\,\cos x\,(1-2\sin^2 x)=0 and answer the following. (i) Solve 2sin⁡x cos⁡x=02\sin x\,\cos x = 0 and write its general solution. (ii) Solve 1−2sin⁡2x=01-2\sin^2 x = 0 and write its general solution. (iii) Using the results of (i) and (ii), obtain the complete general solution of the given equation. (iv) Find the number of distinct solutions in [0,2π)[0,2\pi) and list them in ascending order.

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