If sin A + sin2 A = 1,

Question:

If sin A + sin2 A = 1, then the value of (cos2 A + cos4 A) is

(a) 1

(b) $\frac{1}{2}$

(c) 2

(d) 3

 

Solution:

(a) Given $\sin A+\sin ^{2} A=1$

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

On squaring both sides, we get 

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

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

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

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