If sin x + cos x = a, find the value of sin6 x + cos6 x.

Given, sin x + cos x = a


We need to find the value of the expression,


sin6 x + cos6 x = (sin2 x)3 + (cos2 x)3


= (sin2 x + cos2 x)3 – 3 sin2 x cos2 x (sin2 x + cos2 x)


[ by using the formula a3 + b3 = (a+b)3 – 3ab(a+b)]


= (1)3 – 3 sin2 x cos2 x (1)


[ by using the formula sin2 x + cos2 x = 1]




[ by using the formula sin2 x + cos2 x = 1]






Hence sin6 x + cos6 x


1