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verify the identity: sinx-sinxcos^2x=sinx

Using trigonometric identities 

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are you sure about the problem?  sinx-sinxcos^2x is eqypual to sin^3x.

Oops...my bad! Your problem is correct! sinx-sinxcos^2x is eqypual to sin^3x

How can I verify the identity? 

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Daniel O. | Math and Physics Tutor, with a math and physics degreeMath and Physics Tutor, with a math and ...
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sinx - sinx cos2x = sin3x

remember that sin2x + cos2x = 1, so cos2x = 1 - sin2x, and we can substitute that in place of cos2x...

sinx - sinx (1 - sin2x) = sin3x now distribute the sinx into the parentheses...

sinx - (sinx - sin3x) = sin3x

sinx - sinx + sin3x = sin3x

sin3x = sin3x

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You could also factor out sinx from the first two terms in the first line:

sinx - sinx cos2x = sin3x

sinx (1 - cos2x) = sin3x

sinx (sin2x) = sin3x

sin3x = sin3x