Embibe Experts Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: TS EAMCET 2020 (9-Sep Shift-1)

Match the items of List-I with those of the items of List-II

Let $Z$ denote the set of integers. Then match the items in list-$\mathrm{I}$, with those of the items in List-$\mathrm{II}$

The correct match is

$2{\tan }^{-1}\frac{1}{5}+{\sec }^{-1}\frac{5\sqrt{2}}{7}+2{\tan }^{-1}\frac{1}{8}=$

If ${\sin }^{-1}x<{\cos }^{-1}x,$ then

If ${\sin }^{-1}\left(\frac{x}{5}\right)+{\mathrm{cosec}}^{-1}\left(\frac{5}{4}\right)=\frac{\pi }{2},$ then $5+x=$

$\sin \left({\tan }^{-1}\frac{4}{5}+{\tan }^{-1}\frac{4}{3}+{\tan }^{-1}\frac{1}{9}-{\tan }^{-1}\frac{1}{7}\right)=$

If $f\left(n\right)=\tan \left[{\tan }^{-1}\frac{1}{1+2}+{\tan }^{-1}\frac{1}{1+6}+{\tan }^{-1}\frac{1}{1+12}+...+{\tan }^{-1}\frac{1}{1+n(n+1)}\right]$
then $f\left(2021\right)=$