Trigonometric Treasure $\rightarrow 4!$

If, $\sin 7x = \cos 11x$

Then, $\sin 7x = \sin (90 - 11x)$

$7x = 90 - 11x$

$18x = 90$

$x=5$

Substituting the value of x, we get

$\tan 9(5) + \cot 9(5)$

$\tan 45 + \cot 45$

$1 + 1$ = $2$