trigonometry - Finding the reciprocals using trigonometric functions and their inverses

If $x\neq0$, how to find the reciprocal of $x$ only by using trigonometric functions and inverse trigonometric functions?

I have found only one answer, which is;
$\tan (\cos ^{-1}(\sin(\tan^{-1}(x))))=\frac{1}{x}$.

Is there any other answer?

Answer

HINT

Recall that

$$\arctan x = \frac{\pi}2-\arctan \frac1x$$

$$\arctan x = -\frac{\pi}2-\arctan \frac1x$$