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August 25, 2016
Posted by **Zack** on Sunday, May 5, 2013 at 11:16am.

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

- Advanced Functions/Trig -
**Reiny**, Sunday, May 5, 2013 at 1:02pmLS = cos^4 x + sin^4 x

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

= 1 - 2(sin^2 x)(cos^2 x) , now recall sin(2x) = 2sinxcosx

= 1 - (2sinxcosx)(sinxcosx)

= 1 - sin(2x) (1/2)sin(2x)

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

= RS