Question

If cos A + cos² A = 1, then (sin² A + sin⁴ A) = ?
(a) 1
(b) 2
(c) 3
(d) 4

Answer 1

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