Embibe Experts Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: Exercise 1

Consider the following statements

$\mathrm{I}.$ ${\tan }^{-1}1+{\tan }^{-1}(0.5)=\mathrm{\pi }/2$

$\mathrm{II}.$ ${\sin }^{-1}(1/3)+{\cos }^{-1}(1/3)=\mathrm{\pi }/2$

Which of the above statement($s$) is / are correct?

What is ${\sin }^{-1}\left(\sin \frac{3\mathrm{\pi }}{5}\right)$ equal to?

What is the value of $\sin \left({\sin }^{-1}\left(\frac{3}{5}\right)+{\sin }^{-1}\left(\frac{4}{5}\right)\right)$ ?

If ${\sin }^{-1}1+{\sin }^{-1}\frac{4}{5}={\sin }^{-1}x,$ then what is the value of $x ?$

What is ${\tan }^{-1}\left(\frac{1}{2}\right)+{\tan }^{-1}\left(\frac{1}{3}\right)$ equal to?

If $x$ and $y$ are positive and$xy>1,$ then what is ${\tan }^{-1}x+{\tan }^{-1}y$ equal to?

What is ${\sin }^{-1}\left(\frac{3}{5}\right)+{\sin }^{-1}\left(\frac{4}{5}\right)$ equal to?

The equation ${\tan }^{-1}(1+x)+{\tan }^{-1}(1-x)=\frac{\mathrm{\pi }}{2}$ is satisfied by