cos^6x + 3sin^2x × cos^2x + sin^6x = 1 Buktikan identitas trigonometrinya!

Verifying Identity Trigonometry.

a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)
(a² + 2ab + b²) = (a + b)²

cos⁶ x + 3 sin² x cos² x + sin⁶ x
= (cos⁶ x + sin⁶ x) + 3 sin² x cos² x
= (cos² x + sin² x)(cos⁴ x - cos² x sin² x + sin⁴ x) + 3 sin² x cos² x
= 1 (cos⁴ x + 2 sin² x cos² x + sin⁴ x)
= (cos² x + sin² x)²
= 1²
= 1
Proven.