Question

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

• A. $-1$
• B. $1$
• C. $0$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$1$

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

Squaring on both sides

$⟹({\cos }^{2}x{)}^2={\sin }^{2}x$

$⟹{\cos }^{4}x=1-{\cos }^{2}x$

$⟹{\cos }^{4}x+{\cos }^{2}x=1$

$⟹{\cos }^{2}x(1+{\cos }^{2}x)=1$