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

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1 Answer

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

Comments

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