Question

$sin^{6} x + cos^{6} x = ?$

Answer 1

sin^6x+cos^6x = (sin² x)³+(cos²x)³ = (sin²x+cos²x)(sin⁴x-sin²x*cos²x+cos⁴x) = sin⁴x+2sin²x*cos²x+cos⁴x-3sin²x*cos²x = (sin²x+cos²x)²-3sin²x*cos²x = 1-3sin²x*cos²x