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How do you simplify the expression $cos x (sec x - cos x)$ $cosx(secx-cosx)$ ?

1 Answer

Shwetank Mauria

Oct 6, 2016

$cos x (sec x - cos x) = {sin}^{2} x$ $cosx(secx-cosx)=sin^2x$

Explanation:

$cos x (sec x - cos x)$ $cosx(secx-cosx)$

= $cos x (\frac{1}{cos x} - cos x)$ $cosx(1/cosx-cosx)$

= $cos \times x \frac{1}{cos x} - {cos}^{2} x$ $cosxxx1/cosx-cos^2x$

= $1 - {cos}^{2} x$ $1-cos^2x$

= ${sin}^{2} x$ $sin^2x$

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