Asked by Anonymous
simplify the expression to a single term:
(1-2Sin^2 X)^2 + 4sin^2 X Cos^2 X
I'm not sure how to start this or which identities to use. Any suggestions?
(1-2Sin^2 X)^2 + 4sin^2 X Cos^2 X
I'm not sure how to start this or which identities to use. Any suggestions?
Answers
Answered by
Reiny
(1-2Sin^2 X)^2 + 4sin^2 X Cos^2 X
(sin^2 x + cos^2 x - 2sin^2 x)^2 + (2sinxcosx)^2
= (cos^2x - sin^2x)^2 + (sin 2x)^2
= (cos 2x)^2 + (sin 2x)^2
= 1
(sin^2 x + cos^2 x - 2sin^2 x)^2 + (2sinxcosx)^2
= (cos^2x - sin^2x)^2 + (sin 2x)^2
= (cos 2x)^2 + (sin 2x)^2
= 1
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