Vinod Singh and Shweta Pawar Solutions for Chapter: Trigonometric Functions-II, Exercise 4: Evaluation Test

If ${\sin }^{-1}\left(\sin \frac{33\pi }{7}\right)+{\cos }^{-1}\left(\cos \frac{46\pi }{7}\right)+{\tan }^{-1}\left(-\tan \frac{13\pi }{8}\right)+{\cot }^{-1}\left(-\cot \frac{19\pi }{8}\right)=\frac{a\pi }{b},$ where $a$ and $b$ are constants, then $(a+b)$ is equal to

${\sin }^{-1}\frac{4}{5}+{\sin }^{-1}\frac{5}{13}+{\sin }^{-1}\frac{16}{65}$ is equal to

If $A=2 {\tan }^{-1}(2\sqrt{2}-1)$ and $B=3 {\sin }^{-1}\left(\frac{1}{3}\right)+{\sin }^{-1}\left(\frac{3}{5}\right)$, then

If  ${\cot }^{-1}x+{\cot }^{-1}y+{\cot }^{-1}z=\frac{\pi }{2}$ & $x,y,z>0$, then $x+y+z$ is equal to

The principal value of ${\cos }^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9\pi }{10}-\sin \frac{9\pi }{10}\right)\right\}$ is

${\tan }^{-1}1+{\tan }^{-1}2+{\tan }^{-1}3$ is equal to

If ${\tan }^{-1}\frac{1}{1+2x}+{\tan }^{-1}\frac{1}{4x+1}={\tan }^{-1}\frac{2}{x^2}$ where $x>0$, then $x$ is equal to

If ${\cot }^{-1}x+{\sin }^{-1}\frac{1}{\sqrt{5}}=\frac{\pi }{4}$ & $x>1$, then $x$ is equal to