Homework SourseProve these identities A sinx cosx2 1 sin2x B cos4 x sin4
Prove these identities
A.) (sinx+ cosx)^2 = 1 + sin2x
B.) cos^4 x - sin^4 x = cos2x
Please show all work, i struggle with this!!!
Prove these identities
A.) (sinx+ cosx)^2 = 1 + sin2x
B.) cos^4 x - sin^4 x = cos2x
Please show all work, i struggle with this!!!
A.) (sinx+ cosx)^2 = 1 + sin2x
B.) cos^4 x - sin^4 x = cos2x
Please show all work, i struggle with this!!!
Solution
A.) (sinx+ cosx)^2 = 1 + sin2x
.(sinx+ cosx)^2 = sin^2x + cos^2 x + 2sinxcosx
= 1 + sin2x [ sin^2x + cos^2 x =1 and 2sinxcosx = sin2x
B.) cos^4 x - sin^4 x = cos2x
cos^4 x - sin^4 x = (cos^2 x - sin^2x )(cos^2 x+sin^2x )
= cos2x * 1
= cos2x
