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 
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