Milena C.

asked • 01/24/13

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

Using trigonometric identities 

Kevin C.

tutor

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

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01/24/13

Milena C.

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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01/24/13

1 Expert Answer

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Daniel O. answered • 01/24/13

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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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Daniel O.

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

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01/25/13

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