Prove that si^4 0 + cos^4 0 = 1 - 2 sin^2 0 cos²0.
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sin^4 x + cos^4 x
= (sin^2 x)^2 + (cos^2 x)^2
[ Using a^2 + b^2 = (a + b)^2 - 2ab) ]
= (sin^2 x + cos^2 x)^2 - 2* sin^2 x* cos^2 x
= 1 - 2* sin^2 x* cos^2 x
Hence Proved
= (sin^2 x)^2 + (cos^2 x)^2
[ Using a^2 + b^2 = (a + b)^2 - 2ab) ]
= (sin^2 x + cos^2 x)^2 - 2* sin^2 x* cos^2 x
= 1 - 2* sin^2 x* cos^2 x
Hence Proved
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