Question

If $\cos A+{\cos }^{2}A=1$, then the value of ${\sin }^{2}A+{\sin }^{4}A$ is

• A. $1$
• B. $\frac{1}{2}$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$1$

$\cos A+{\cos }^{2}A=1$.........( 1 )

$cosA=1-{\cos }^{2}A={\sin }^{2}A$

Now,

${\sin }^{2}A+{\sin }^{4}A=\cos A+\left({\cos }^{2}A\right)$...............($\because cosA=si{n}^{2}A)$

$={\sin }^{2}A+{\sin }^{4}A=1$........$\left(from1\right)$