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Trigonometric functions (prove equalities)?

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can anyone help me with this...

i have to prove that the left side = the right side...

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

thanks~

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  1. [sin^2A]^2 - [cos^2A]^2 = 2sin^2A -1

    LHS > using X^2 - Y^2 = (X+Y) (X-Y)

    [sin^2A + cos^2 A][sin^2 A - cos^2A]

    [1] [sin^2 A - (1- sin^2 A)]

    = 2 sin^2 A - 1 = RHS

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