Question

cos²(π/4-x) -sin²(π/4-x) =sin2x
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Answer 1

Answer:

$l.h.s. = {cos}^{2} ( \frac{\pi}{4} - x) - {sin}^{2} ( \frac{\pi}{4} - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: = cos(2( \frac{\pi}{4} - x)) = \cos( \frac{\pi}{2} - 2x) \\ \: \: \: \: \: \: \: \: \: \: \: = sin(2x)$

hence proved