The general solution of the equation $si{n}^{50}x-{\cos }^{50}x=1$ is

The correct option is C
We have,
${\sin }^{50}x-{\cos }^{50}x=1$
$\Rightarrow {\sin }^{50}x=1+{\cos }^{50}x$
Since, ${\sin }^{50}x\le 1$ and ${\cos }^{50}x\ge 1,$ therefore, the two sides are equal only if
${\sin }^{50}x=1=1+{\cos }^{50}x$ i.e., ${\sin }^{50}x=1and{\cos }^{50}x=0$
$\therefore x=n\pi +\frac{\pi }{2},n\in I$