Question

If $\cos x+{\cos }^{2}x=1$, prove that ${\sin }^{2}x+{\sin }^{4}x=1$.

Answer 1

Given, $cosx+co{s}^{2}x=1$
$\Rightarrow cosx=1-co{s}^{2}x$
$\Rightarrow cosx=si{n}^{2}x$
Squaring both sides we get
$\Rightarrow co{s}^{2}x=si{n}^{4}x$ .....(1)
$\Rightarrow si{n}^{4}x-co{s}^{2}x=0$
Adding both side 1, we get
$\Rightarrow si{n}^{4}x+1-co{s}^{2}x=1$
$\therefore si{n}^{2}x+si{n}^{4}x=1$ Proved.