Posted by **skye** on Thursday, August 16, 2012 at 11:24pm.

use power reducing identities to prove the identity

sin^4x=1/8(3-4cos2x+cos4x)

cos^3x=(1/2cosx) (1+cos2x)

thanks :)

- precalc -
**Steve**, Friday, August 17, 2012 at 12:21am
cos 2x = 2cos^2 x - 1

so, 1/2 cos x (1+2cos^2 x - 1) = cos^3 x

cos 4x = 1 - 2sin^2 2x

= 1 - 8sin^2 x cos^2 x

= 1 - 8sin^2 x (1 - sin^2 x)

= 1 - 8sin^2 x + 8 sin^4 x

cos 2x = 1 - 2sin^2 x

4cos 2x = 4 - 8sin^2 x

1/8(3-4cos2x+cos4x)

= 1/8(3 - 4 + 8sin^2 x + 1 - 8sin^2 x + 8 sin^4 x)

= 1/8(8sin^4 x)

= sin^4 x

## Answer This Question

## Related Questions

- trig - I keep trying to find the power reducing formula for sin^4(x), but I can'...
- Math - Trig - Double Angles - Prove: cos4x = 8cos^4x - 8cos^2x + 1 My Attempt: ...
- calc - Where do I start to prove this identity: sinx/cosx= 1-cos2x/sin2x please ...
- Trig - prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= ...
- Precalculus with Trigonometry - Prove or disprove the following identity: (sin(...
- trig - how can you confirm the identity cos^4x = (1/8)(3+ 4cos2x+ cos4x) and ...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- Math - Calculus - The identity below is significant because it relates 3 ...
- Mathematics - Trigonometric Identities - Prove: sin^2x - sin^4x = cos^2x - cos^...
- trigonometry - Verify that following are identities: 1. cos 3t = 4 cosł t-3 cos ...

More Related Questions