Prove this identity sinx4cosx412cosx2Solutionsin4xcos4x sin2

Prove this identity

sin(x)⁴-cos(x)⁴=1-2cos(x)²

sin⁴(x)-cos⁴(x)

=(sin²(x))²-(cos²(x))²

(a²-b²)=(a+b)(a-b)

=(sin²(x) +cos²(x))(sin²(x) -cos²(x))

[since sin²(x) +cos²(x) =1 is an identity =>sin²(x) =1-cos²(x)]

=(1)((1-cos²(x)) -cos²(x))

=1-2cos²(x)

Prove this identity sin(x)4-cos(x)4=1-2cos(x)2Solutionsin4(x)-cos4(x) =(sin2(x))2-(cos2(x))2 (a2-b2)=(a+b)(a-b) =(sin2(x) +cos2(x))(sin2(x) -cos2(x)) [since sin

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