Mathematics

Problem

Solve the equation

2\sin x\,\cos x\,(1-2\sin^2 x)=0

and answer the following. a. (i) Solve

2\sin x\,\cos x = 0

and write its general solution. b. (ii) Solve

1-2\sin^2 x = 0

and write its general solution. c. (iii) Using the results of (i) and (ii), obtain the complete general solution of the given equation. d. (iv) Find the number of distinct solutions in

[0,2\pi)

and list them in ascending order.

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