Question

If sin A + sin² A = 1, then (cos² A + cos⁴ A) = ?
(a) $\frac{1}{2}$
(b) 1
(c) 2
(d) 3

Answer 1

(b) 1
$\begin{array}{l}\text{sin}A+{\text{sin}}^{2}A=1\\ \text{=>sin}A=1-{\text{sin}}^{2}A\\ =>\text{sin}A={\text{cos}}^{2}A(\because \text{1}-{\text{sin}}^{2}A)\\ =>{\text{sin}}^{2}A={\text{cos}}^{4}A\left(\text{Squaring both sides}\right)\\ \text{=>1}-{\text{cos}}^{2}A={\text{cos}}^{4}A\\ {\text{=> cos}}^{4}A+{\text{cos}}^{2}A=1\end{array}$