Question

sin^6x+cos^6x=1-3sin^2xcso^2x prove that​

Answer 1

We know that

$( { { \sin(x) }^{2} + { \cos(x) }^{2} ) }^{3} = { \sin(x) }^{6} + { \cos(x) }^{6} + 3 { \sin(x) }^{2} { \cos(x) }^{2} \times 1 \\ so \\ { \sin(x) }^{6} + { \cos(x) }^{6} = 1 - 3 { \sin(x) }^{2} \times { \cos(x) }^{2}$