Mark the Correct alternative in the following:

The value of cos⁴ x + sin⁴ x – 6 cos² x sin² x is

A.cos 2x

B. sin 2x

C. cos 4x

D. 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

The answer is option A.