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Question

If sin x + cos x = a, find the value of sin6x+cos6x.

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Solution

sin x + cos x = a

squaring above equation gives a21

= sin 2x = 2 sin x cos x

(sin2x+cos2x)3=sin6x+cos6x+3 sin2 x cos2 x1=sin6x+cos6x+34(2 sin x cos x)2So, sin6x+cos6x=134(a21)2


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