Question

If $sinx+si{n}^{2}x=1$, P.T. ${cos}^{2}x+{cos}^{4}x=1$

Answer 1

$\sin x+{\sin }^{2}x=1$ ......$\left(1\right)$

$\Rightarrow \sin x=1-{\sin }^{2}x={\cos }^{2}x$

$\Rightarrow \sin x={\cos }^{2}x$ ......$\left(2\right)$

$\Rightarrow {\sin }^{2}x={\cos }^{4}x$ .........$\left(3\right)$

Now, ${\cos }^{2}x+{\cos }^{4}x=1$

$\Rightarrow \sin x+{\sin }^{2}x=1$ from $\left(2\right)$ and $\left(3\right)$

Hence proved.