Mark the Correct alternative in the following:
The value of cos4 x + sin4 x – 6 cos2 x sin2 x is
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
The answer is option A.