Q. 29

# Mark the Correct alternative in the following:The value of cos4 x + sin4 x – 6 cos2 x sin2 x isA.cos 2xB. sin 2xC. cos 4xD. None of these

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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