Solve: ${\sin }^{-1}\frac{5}{\mathrm{x}}+{\sin }^{-1}\frac{12}{\mathrm{x}}=\frac{\mathrm{\pi }}{2}$

Important Questions on Inverse Trigonometric Functions

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

$\cos \left(2\left({\tan }^{-1}\frac{1}{5}+{\tan }^{-1}5\right)\right)=\_\_\_\_\_\_\_.$

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

${\cot }^{-1}\left(21\right)+{\cot }^{-1}\left(13\right)+{\cot }^{-1}(-8)=$

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

$cosec\left[2{\cot }^{-1}\left(5\right)+{\cos }^{-1}\left(\frac{4}{5}\right)\right]$ is equal to:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If ${\sin }^{-1}x{\cos }^{-1}x=p$, then the value of ${\left({\sin }^{-1}x\right)}^3+{\left({\cos }^{-1}x\right)}^3$ is

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The value of $\cot \left(\sum _{n=1}^{19}{\cot }^{-1}\left(1+\sum _{p=1}^{n}2p\right)\right)$ is:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

${\sin }^{-1}\left(\cos \left({\sin }^{-1}x\right)\right)+{\cos }^{-1}\left(\sin \left({\cos }^{-1}x\right)\right)=$

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If $\frac{{\sin }^{-1}x}{a}=\frac{{\cos }^{-1}x}{b}=\frac{{\tan }^{-1}y}{c}; 0<x<1,$ then the value of $\cos \left(\frac{\pi c}{a+b}\right)$ is:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If $y\left(x\right)={\cot }^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right), x\in \left(\frac{\pi }{2},\pi \right)$, then $\frac{dy}{dx}$ at $x=\frac{5\pi }{6}$ is:

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

$\cos \left[2{\sin }^{-1}\frac{3}{4}+{\cos }^{-1}\frac{3}{4}\right]=$

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If ${\sin }^{-1}x-{\cos }^{-1}x=\frac{\pi }{6},$ then the value of $x$ is

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If ${\left({\sin }^{-1}x\right)}^2-{\left({\cos }^{-1}x\right)}^2=a; 0<x<1, a\ne 0,$ then the value of $2x^2-1$ is

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The solution of ${\tan }^{-1}2x+{\tan }^{-1}3x=\frac{\pi }{4}$ is

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

${\cos }^{-1}\left(\cos \right(-5\left)\right)+{\sin }^{-1}\left(\sin \right(6\left)\right)-{\tan }^{-1}\left(\tan \right(12\left)\right)$ is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

${\tan }^{-1}\left(\cot x\right)+{\cot }^{-1}\left(\tan x\right)=$ (where, $0<x<\frac{\pi }{2}$)

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

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

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

Find the value of ${\tan }^{-1}\left(\sqrt{3}\right)-{\cot }^{-1}(-\sqrt{3})$.

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

The value of $\sin \left(2{\tan }^{-1}\frac{1}{3}\right)+\cos \left({\tan }^{-1}2\sqrt{2}\right)$ will be

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If ${\sin }^{-1}x+{\cos }^{-1}y=2\pi /5$, then ${\cos }^{-1}x+{\sin }^{-1}y$ is

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

If $a+\frac{\pi }{2}<2 {\tan }^{-1}x+3 {\cot }^{-1}x<b$ then $\text{'}a\text{'}$ and $\text{'}b\text{'}$ are respectively.

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Properties of Inverse Trigonometric Functions

${\sin }^{-1}\frac{3}{5}-{\sin }^{-1}\frac{8}{17}=$