Question

If $\sin x=$ ${\cos }^{2}x$, then ${\cos }^{2}x(1+{\cos }^{2}x)$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

The correct option is B $1$

Given, $\sin x={\cos }^{2}x$

Thus $\sin x=1-{\sin }^{2}x$

$\Rightarrow {\sin }^{2}x+\sin x=1$ ....(1)

We need to find value of ${\cos }^{2}x(1+{\cos }^{2}x)$

$\Rightarrow \sin x(1+\sin x)$

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

From the equation (1), we have

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

Option B is correct.