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August 23, 2014

August 23, 2014

Posted by **Hannah** on Sunday, February 28, 2010 at 12:27pm.

sin x(1 - 2 cos^2 x + cos^4 x) = sin^5 x

1-2cos^2 x looks like 2cos^2x-1 its just backwards. I am not sure where to start.

- Pre-Cal -
**Reiny**, Sunday, February 28, 2010 at 12:46pmgood observation

recall that cos 2A = 2cos^2 A - 1 = 1 - 2sin^2 A

so 1 - 2 cos^2 x = 2sin^2 x - 1

LS

=sin x(1 - 2 cos^2 x + cos^4 x)

= sinx(2sin^2 x - 1 + (cos^2x)(cos^2x)

= sinx( 2 sin^2x - 1 + (1-sin^2x)(1 -sin^2x))

= sinx(2sin^2x - 1 + 1 - 2sin^2x + sin^4x)

= sinx(sin^4x)

= sin^5 x

= RS

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