Trig

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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?

  • Trig -

    (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

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