If sin x = cos


If sin x = cos2 x, then write the value of cos2 x (1 + cos2 x).


We have:

$\sin x=\cos ^{2} x$    ...(1)

$\therefore \cos ^{2} x\left(1+\cos ^{2} x\right)$

$=\sin x(1+\sin x) \quad[\operatorname{Using}(1)]$

$=\sin x+\sin ^{2} x$

$=\sin x+1-\cos ^{2} x$

$=\sin x+1-\sin x$      [Using (1)]

= 1

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