[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
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{cos(\theta )=\sqrt{1-sin^2(\theta)}}\qquad\qquad and
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{cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})}\\\\
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[/tex]
[tex]\bf \cfrac{cos^2(\pi -x)}{\sqrt{1-sin^2(x)}}\implies \cfrac{[cos(\pi -x)]^2}{cos(x)}
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\cfrac{[cos(\pi )cos(x)-sin(\pi )sin(x)]^2}{cos(x)}\qquad
\begin{cases}
cos(\pi )=-1\\
sin(\pi )=0
\end{cases}\qquad thus
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\cfrac{[\boxed{-1}cos(x)-\boxed{0}sin(x)]^2}{cos(x)}\implies \cfrac{[-cos(x)]^2}{cos(x)}\implies \cfrac{[cos(x)]^2}{cos(x)}
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\cfrac{cos^2(x)}{cos(x)}\implies cos(x)[/tex]
