Question

If ${\sin }^{2}x+{\cos }^{2}y=2se{c}^2$ z then x, y, z are ______.

Answer 1

Here L.H.S. $\le 2$ and R.H.S. $\ge 2$.
The equation will hold when we have only sign of equality and in that case
${\sin }^{2}x=1$, ${\cos }^{2}y=se{c}^{2}z=1$
or ${\cos }^{2}x=0$, ${\sin }^{2}y=0,{\cos }^{2}z=1$
or $\sin 62z=0$
$\therefore x=(n+\frac{1}{2})\pi ,y=m\pi ,z=r\pi$.