Question

$2 sin^{2} (2x) - 1 = 0$
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Answer 1

$2sin^22x-1=0\\sin^22x=frac{1}{2}; ; ,qquad Big [; sin^2a=frac{1-cos2a}{2}; Big ]\\frac{1-cos4x}{2}=frac{1}{2}\\1-cos4x=1\\cos4x=0\\4x=frac{pi }{2}+pi n; ,; nin Z\\x=frac{pi }{8}+frac{pi n}{4}; ,; nin Z$