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The value of cos4 x + sin4 x – 6 cos2 x sin2 x isA. cos 2xB. sin 2xC. cos 4xD. None of these

Answer»

Correct answer is A.

Given expression is cos4 x + sin4 x – 6 cos2 x sin2 x

= [(cos2x)2 + (sin2x)2 - 2 cos2x sin2x] - 4 cos2x sin2x

[using the formula a2 + b2 = (a + b)2 - 2ab]

= (cos2x - sin2x)2 - 4 cos2x sin2x

[using the formula cos 2x = cos2 x – sin2 x]

= (cos2x)2 – (2 sinx cosx )2

[ using the formula sin 2x = 2 sin x cos x ]

= (cos 2x)2 – (sin 2x)2

[ using the formula cos 2x = cos2 x – sin2 x ]

= cos 4x

Therefore cos4 x + sin4 x – 6 cos2 x sin2 x = cos 4x



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