If $x=\sin \left(2{\tan }^{-1}2\right)$ and $y=\sin \left(\frac{1}{2}{\tan }^{-1}\frac{4}{3}\right)$, then

Important Questions on Inverse Circular Functions

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 20

The set of values of $a$ for which $x^2+ax+{\sin }^{-1}\left(x^2-4x+5\right)+{\cos }^{-1}\left(x^2-4x+5\right)=0$ has at least one solution is

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 21

If ${\tan }^{-1}\left(x+h\right)={\tan }^{-1}\left(x\right)+\left(h \sin y\right)\left(\sin y\right)-{\left(h\sin y\right)}^2·\frac{{\sin }^{2}y}{2}+{\left(h\sin y\right)}^3·\frac{{\sin }^{3}y}{3}+\dots$ where $x\in \left(0,1\right),y\in \left(\frac{\pi }{4},\frac{\pi }{2}\right)$, then

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 22

Solution set of $[{\sin }^{-1}x]>[{\cos }^{-1}x],$ where [.] denotes the greatest integer function, is

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 23

The number of real solutions of $\left(x, y\right)$ where $y=\left|\sin x\right|,$ $y={\cos }^{-1}\left(\cos x\right),$ $-2\pi \le x\le 2\pi ,$ is

HARD

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 24

If ${\sin }^{-1}x+{\sin }^{-1}y+{\sin }^{-1} z=\frac{3\pi }{2}$ and $f\left(1\right)=2, f\left(p+q\right)=f\left(p\right). f\left(q\right) \forall p, q \in R,$ then

$x^{f\left(1\right)}+y^{f\left(2\right)}+z^{f\left(3\right)}- \frac{x+y+z}{x^{f\left(1\right)}+y^{f\left(2\right)}+z^{f\left(3\right)}}=$

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 25

If ${\tan }^{-1}x+{\tan }^{-1}2x+{\tan }^{-1}3x=\pi ,$ then

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 26

The number of real solution of ${\tan }^{-1}\sqrt{x(x+1)}+{\sin }^{-1}\sqrt{x^2+x+1}=\frac{\pi }{2}$ is

MEDIUM

Mathematics

IMPORTANT

TRIGONOMETRY FOR JEE MAIN AND ADVANCED>Chapter 13 - Inverse Circular Functions>EXERCISE>Q 27

If $\sum _{i=1}^{2n}{\cos }^{-1}{x}_i=0$, then $\sum _{i=1}^{2n}{x}_i$ is