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

The correct option is C

$si{n}^{50}x=1+co{s}^{50}x$
Since $si{n}^{50}x\le 1andco{s}^{50}x\le 1$ therefore the two sides are equal if and only if
$si{n}^{50}x=1andco{s}^{50}x=0$
$\therefore x=n\pi +\frac{\pi }{2},n\in I$