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How do you simplify Sin^2xcos^2x-cos^2x ? -Thanks

1 Answer

Jan 16, 2018

It simplifies to $- {cos}^{4} x$ $-cos^4x$

Explanation:

${sin}^{2} x {cos}^{2} x - {cos}^{2} x$ $sin^2xcos^2x-cos^2x$

${cos}^{2} x ({sin}^{2} x - 1)$ $cos^2x(sin^2x - 1)$

We know that ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x + cos^2x = 1$ , so
${sin}^{2} x - 1 = - {cos}^{2} x$ $sin^2x -1 = -cos^2x$
Therefore:

${cos}^{2} x (- {cos}^{2} x)$ $cos^2x(-cos^2x)$

$- {cos}^{4} x$ $-cos^4x$

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