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