Suppose $S_a(x) = \operatorname{Sec}^{-1}\left(\frac{x}{a}\right) + \operatorname{Sec}^{-1}(a)$ for $a \neq 0$. If $S_a(x) = S_b(x)$ for $a \neq b$,then $x =$

Show that $\sin ^{-1} \frac{3}{5}-\sin ^{-1} \frac{8}{17}=\cos ^{-1} \frac{84}{85}$

If ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y + {\cos ^{ - 1}}z = 3\pi ,$ then $xy + yz + zx = $

If $y = \tan^{-1}(\sec x^3 - \tan x^3)$ and $\frac{\pi}{2} < x^3 < \frac{3\pi}{2}$,then:

Consider the following statements:
Assertion $(A)$: For $x \in \mathbb{R}-\{1\}$, $\frac{d}{dx}\left(\tan^{-1}\left(\frac{1+x}{1-x}\right)\right) = \frac{d}{dx}\left(\tan^{-1} x\right)$.
Reason $(R)$: For $x < 1$, $\tan^{-1}\left(\frac{1+x}{1-x}\right) = \frac{\pi}{4} + \tan^{-1} x$, and for $x > 1$, $\tan^{-1}\left(\frac{1+x}{1-x}\right) = -\frac{3\pi}{4} + \tan^{-1} x$.
The correct answer is:

The differential coefficient of $\cos^{-1} \left( \sqrt{\frac{1+x}{2}} \right)$ with respect to $x$ is