Solution
Given,
$$2 \sin^2 x - 1 = 0$$
$$=$$> $$2\sin^2x=1$$
$$=$$> $$\sin^2x=\frac{1}{2}$$
$$=$$> $$\sin x=\frac{1}{\sqrt{2}}$$
$$=$$> $$\sin x=\sin\frac{\pi\ }{4}$$
$$=$$> $$x=\frac{\pi}{4}$$
Hence, the correct answer is Option A
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