$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

$A$ positive acute angle is divided into two parts whose tangents are $\frac{1}{2}$ and $\frac{1}{3}$. Then the angle is

For the equation $\cos ^{-1} |x| + \cos ^{-1} |2x| = \pi$,the number of real solution$(s)$ is

Evaluate the expression: $sec^2(\tan^{-1} 3) - \tan^2(sec^{-1} 3) = $

Let $a, b$ and $c$ be the lengths of the sides of a triangle with its opposite angles $A, B$ and $C$ respectively. If $a=3, b=4$ and $A=\sin^{-1}\left(\frac{3}{4}\right)$,then the angle $B$ is (in $^{\circ}$)

Find the value of $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)$.