If sin A+sin ^{2} A=1, then value of expression left(cos ^{2} A+cos ^{4} Aright) is

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8. Introduction to Trigonometry

hard

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

A

$1$

B

$\frac{1}{2}$

C

$2$

D

$3$

Solution

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

$\Rightarrow$ $\sin A=1-\sin ^{2} A=\cos ^{2} A$ $\left[\because \sin ^{2} \theta+\cos ^{2} \theta=1\right]$

On squaring both sides, we get

$\sin ^{2} A=\cos ^{4} A$

$1-\cos ^{2} A=\cos ^{4} A$

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

Standard 10

Mathematics

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