Question

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

• A. $2$
• B. $1$
• C. $-2$
• D. $0$

Answer 1

Answer: (B)

$1$

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

$\Rightarrow \sin A=1-{\sin }^{2}A$

$\Rightarrow \sin A={\cos }^{2}A$

$\Rightarrow {\cos }^{2}A+{\cos }^{4}A={\cos }^{2}A[1+{\cos }^{2}A]$

$=\sin A[1+\sin A]$

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

$=1$

Hence, the answer is $1.$