Question

Cos^6 x + 3 sin^2 cos^2 x + sin^6 x = 1

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Answer 1

Verified answer

cos⁶ x + 3 sin² x cos² x + sin⁶ x = 1
= (cos² x)³ + 3 sin² x cos² x +(sin² x)³
= (cos² x + sin² x)³ - 3(cos² x)² sin² x  - 3 (cos² x) (sin² x)² + 3 sin² x cos² x
= (1)³ - 3 cos² x sin² x ( cos² x + sin² x)  + 3 sin² x cos² x
= (1)³ - 3 cos² x sin² x (1) + 3 sin² x cos² x
= (1)³ - 0
= 1