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