Question

If cos A + cos² A = 1, then (sin² A + sin4 A) = ?
(a) $\frac{1}{2}$
(b) 2
(c) 1
(d) 4

Answer 1

$$\begin{gathered} \begin{array}{l}(c)\; 1\\ \mathrm{}\mathrm{cosA}{+}^2\mathrm{A}\mathrm{=1}\end{array} \\ \mathrm{=>}\cos \mathrm{A}{\mathrm{=sin}}^2\mathrm{A}...\left(\mathrm{i}\right) \\ \mathrm{Squaring\; both\; sides}of\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}: \\ {\cos }^2\mathrm{A}={\sin }^4\mathrm{A}...\left(\mathrm{ii}\right) \\ \mathrm{A}\mathrm{dding}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ {\sin }^2\mathrm{A}+{\sin }^4\mathrm{A}=\cos \mathrm{A}+{\cos }^2\mathrm{A} \\ {\mathrm{=>sin}}^2\mathrm{A}+{\sin }^4\mathrm{A}=1[\because \cos \mathrm{A}{\mathrm{+cos}}^2\mathrm{A}\mathrm{=1}] \end{gathered}$$