Inverse Trigono...

Assertion(A): $$\cos^{-1}x$$ and $$\tan^{-1}x$$ are positive for all positive real values of $$x$$ in their domain.
Reason(R): The domain of $$f(x)=\cos^{-1}x+\tan^{-1}x$$ is $$[-1, 1].$$

The number of solutions of:
$$\displaystyle \sin^{-1}(1+b+b^{2}+\ldots.\infty)+\cos^{-1}(a-\frac{a^{2}}{3}+\frac{a^{3}}{9}+\ldots\infty)=\frac{\pi}{2}$$

If $$(\tan^{-1}x)^{2}+(\cot^{-1}x)^{2} = \displaystyle \frac{5\pi^{2}}{8}$$, then $$x=$$

$$cos^{-1} \left (\sqrt{\dfrac{a-x}{a-b}} \right)$$ =$$sin^{-1} \left (\sqrt{\dfrac{x-b}{a-b}}\right)$$ is possible if

If $$\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma =\displaystyle \frac{3\pi}{2}$$, then $$\alpha\beta+\alpha\gamma+\beta\gamma$$ is equal to :

The solution set of the equation $$\tan^{-1}x -\cot^{-1}x =\cos^{-1}(2-x)$$ is

The number of real solutions of $$tan^{-1} (\sqrt{x(x+1)}+sin^{-1} \displaystyle \sqrt{(x^{2}+x+1)}=\dfrac{\pi}{2}$$ is

The number of positive integral solutions of the equation  $$tan^{-1}x+cot^{-1}y =tan^{-1} 3$$ is :

If $$(tan^{-1} x)^2 +(cot ^{-1}x)^2=\displaystyle \frac{5 \pi^2}{8}$$, then $$x$$ =

The number of integral solutions of $$sin^{-1}\sqrt{4x-x^{2}-3}+tan^{-1}\sqrt{x^{2}-3x+2}=\frac{\pi }{2}$$ is