cos-2-3pi-2-x-cos-2-x-pi-0-x-pi-x-

Question Number 134331 by Mikael_786 last updated on 02/Mar/21

\cos^{2} (\frac{3 π}{2} - x) = \cos^{2} (x + π)

0 ⩽ x ⩽ π

x = ?

Answered by EDWIN88 last updated on 02/Mar/21

\cos (\frac{3 π}{2} - x) = - \sin x; \cos (x + π) = - \cos x

\Rightarrow {(- \sin x)}^{2} = {(- \cos x)}^{2}

\Rightarrow (\sin x + \cos x) (\sin x - \cos x) = 0

{\begin{cases} \sin x - \cos x = 0 \Rightarrow x = \frac{π}{4} \\ \sin x = - \cos x \Rightarrow x = \frac{3 π}{4} \end{cases}

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