1. ## trigonometry problem

Can someone please explain me how can equation $$sin(\pi -x)+cos^{2}x=1$
$
be solved?

2. $\displaystyle \sin{(\pi - x)} = \sin{x}$.

So the equation reduces to

$\displaystyle \sin{x} + \cos^2{x} = 1$

$\displaystyle \sin{x} + 1 - \sin^2{x} = 1$

$\displaystyle \sin{x} - \sin^2{x} = 0$

$\displaystyle \sin{x}(1 - \sin{x}) = 0$

$\displaystyle \sin{x} = 0$ or $\displaystyle 1 - \sin{x} = 0 \implies \sin{x} = 1$

$\displaystyle x = \pi n$ where $\displaystyle n$ is an integer or $\displaystyle \frac{\pi}{2} + 2\pi m$ where $\displaystyle m$ is an integer.