How do you simplify ${(sin X - cos X)}^{2}$ $(sinX-cosX)^2$ ?

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How do you simplify ${(sin X - cos X)}^{2}$ $(sinX-cosX)^2$ ?

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Answer 1 · 2015-08-20T13:03:31

${(sin X - cos X)}^{2} = 1 - sin 2 X$ $(sinX-cosX)^2 = 1-sin2X$

Explanation:

${sin}^{2} A + {cos}^{2} A = 1$ $sin^2 A + cos^2 A = 1$
$sin 2 A = 2 sin A cos A$ $sin 2A = 2 sin A cos A$

${(sin X - cos X)}^{2} = {sin}^{2} X - 2 sin X cos X + {cos}^{2} X = 1 - 2 sin X cos X = 1 - sin 2 X$ $(sinX-cosX)^2 = sin^2 X -2sin X cos X + cos^2 X = 1-2sin XcosX = 1-sin2X$

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How do you simplify ${(sin X - cos X)}^{2}$ $(sinX-cosX)^2$ ?

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