Question

If cos A + cos² A = 1 then (sin² A + sin⁴ A) = ?
(a) $\frac{1}{2}$

(b) 2

(c) 1

(d) 4

Answer 1

$$\begin{gathered} \mathrm{Given}:\cos A+{\cos }^{2}A=1 \\ \cos A+{\cos }^{2}A=1 \\ \Rightarrow \cos A=1-{\cos }^{2}A \\ \Rightarrow \cos A={\sin }^{2}A\left(\because {\sin }^{2}A+{\cos }^{2}A=1\right) \\ \mathrm{Now}, \\ {\sin }^{2}A+{\sin }^{4}A={\sin }^{2}A+{\left({\sin }^{2}A\right)}^2 \\ =\cos A+{\left(\cos A\right)}^2 \\ =\cos A+{\cos }^{2}A \\ =1 \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{c}\right). \end{gathered}$$