Use the power-reducing identities to write ${sin}^{2} x {cos}^{2} x$ $sin^2xcos^2x$ in terms of the first power of cosine?

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Use the power-reducing identities to write ${sin}^{2} x {cos}^{2} x$ $sin^2xcos^2x$ in terms of the first power of cosine?

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Answer 1 · 2018-03-13T20:46:56

${sin}^{2} x {cos}^{2} x = \frac{1 - cos (4 x)}{8}$ $sin^2xcos^2x=(1-cos(4x))/8$

Explanation:

${sin}^{2} x = \frac{1 - cos (2 x)}{2}$ $sin^2x=(1-cos(2x))/2$

${cos}^{2} x = \frac{1 + cos (2 x)}{2}$ $cos^2x=(1+cos(2x))/2$

${sin}^{2} x {cos}^{2} x = \frac{(1 + cos (2 x)) (1 - cos (2 x))}{4} = \frac{1 - {cos}^{2} (2 x)}{4}$ $sin^2xcos^2x=((1+cos(2x))(1-cos(2x)))/4=(1-cos^2(2x))/4$

${cos}^{2} (2 x) = \frac{1 + cos (4 x)}{2}$ $cos^2(2x)=(1+cos(4x))/2$

$\frac{1 - \frac{1 + cos (4 x)}{2}}{4} = \frac{2 - (1 + cos (4 x))}{8} = \frac{1 - cos (4 x)}{8}$ $(1-(1+cos(4x))/2)/4=(2-(1+cos(4x)))/8=(1-cos(4x))/8$

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Use the power-reducing identities to write ${sin}^{2} x {cos}^{2} x$ $sin^2xcos^2x$ in terms of the first power of cosine?

1 Answer

Explanation:

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Use the power-reducing identities to write ${sin}^{2} x {cos}^{2} x$ $sin^2xcos^2x$ in terms of the first power of cosine?