$\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right) = $

The value of $\cos ^{-1} \left[ \cot \left( \sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}} \right) + \cos ^{-1} \left( \frac{\sqrt{12}}{4} \right) + \sec ^{-1} \sqrt{2} \right]$ is

If $\alpha, \beta$ are the solutions of the equation $\operatorname{Sin}^{-1} x - \operatorname{Cos}^{-1} x = \operatorname{Sin}^{-1}(3x - 2)$ and $\alpha > \beta$,then $3\alpha + 4\beta =$

If $\alpha$ and $\beta$ (where $\alpha > \beta$) are two zeroes of the equation $3\cos^{-1}\left(x^2 - 5x - \frac{11}{2}\right) = \pi$,then $(\alpha^2 + \beta^3)$ is -

If $\sin ^{-1} x + \sin ^{-1}(1-x) = \cos ^{-1} x$, then $x \in$

If the equation $2 \operatorname{Cot}^{-1}(x^2+2x+k) = \pi - 3 \operatorname{Tan}^{-1}(x^2+2x+k)$ has two distinct real solutions,then all the values of $k$ lie in the interval