Buktikan identitas trigonometrinya! cos⁶ x + 3 sin² x cos² x + sin⁶ x = 1

(a² + b²)³ = a^6 + b^6 + 3a²b²(a²+b²)
(a² + b²)³ - 3a²b²(a²+b²) = a^6 + b^6
a^6 + b^6 = (a²+b²)³ - 3a²b²(a²+b²)
nah itu aturannya
dan ingat sin²x + cos²x = 1

cos^6 x + sin^6x + 3 cos²x sin²x
= {(cos²x+sin²x)³ - 3.cos²x.sin²x(cos²x+sin²x)} + 3.cos²x . sin²x
= {(1)³ - 3.cos²x.sin²x(1)} + 3.cos²x.sin²x
= 1 - 3.cos²x.sin²x + 3.cos²x.sin²x
= 1