Value of \()/4 - 2^(-1)3\ is Option 1: 5 Option 2: 6 Option 3: 7 Option 4: 9

Answer: 7. Solution: Let =^(-1)3, so =13 and 2=(2/3)/(1-1/9)=34. Then (()/4-2)=(1-3/4)/(1+3/4)=17, so the cotangent is 7.

Geometry

Trigonometry

Medium

core

Value of $\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}$ is

✅ Correct Option: 3

Let $\theta=\cot^{-1}3$ , so $\tan\theta=\frac13$ and $\tan2\theta=\frac{2/3}{1-1/9}=\frac34$ . Then $\tan\left(\frac{\pi}{4}-2\theta\right)=\frac{1-3/4}{1+3/4}=\frac17$ , so the cotangent is 7.

2026: 18 May Shift 2

Match the LIST-I with LIST-II

LIST-I Functions	LIST-II Principal value
A. $\sin^{-1}\left(\dfrac{1}{2}\right)$	I. $\dfrac{\pi}{4}$
B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	II. $\dfrac{\pi}{6}$
C. $\tan^{-1}(1)$	III. $-\dfrac{\pi}{4}$
D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$	IV. $\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

2025: 21 May Shift 1

Match List-I with List-II

List-I	List-II
(Inverse Trigonometric Function)	(Principal Value)
(A) $\sin^{-1}(-\frac{1}{2})$	(I) ${\pi}/{6}$
(B) $\cos^{-1}(-\frac{1}{2})$	(II) $-{\pi}/{6}$
(C) $\tan^{-1}(-\sqrt{3})$	(III) ${2\pi}/{3}$
(D) $\cot^{-1}(\sqrt{3})$	(IV) $-{\pi}/{3}$

Choose the correct answer from the options given below:

2025: 14 May Shift 2

For $x \in [-1,1]$ , if $4\sin^{-1}x + \cos^{-1}x = \pi$ then $x$ is equal to

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. $\sin^{-1} x + \cos^{-1} x, x \in [-1,1]$	I. $-\frac{\pi}{2}$
B. $\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})$	II. $-\frac{\pi}{6}$
C. $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$	III. $\frac{\pi}{2}$
D. $\sin^{-1}\left(-\frac{1}{2}\right)$	IV. $\frac{\pi}{6}$

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

The value of $\sec^2(\tan^{-1}2) + cosec^2(\cot^{-1}3)$ is:

2022: 4 Aug Shift 1

Match List - I with List - II

List - I	List - II
A. $\tan^{-1}\left(\tan\frac{7\pi}{6}\right)$	I. $\frac{5\pi}{6}$
B. $\tan^{-1}\left(\tan\frac{8\pi}{6}\right)$	II. $\frac{\pi}{2}$
C. $\tan^{-1}\frac{1}{\sqrt{3}} + cosec^{-1}\frac{2}{\sqrt{3}}$	III. $\frac{\pi}{6}$
D. $\cos^{-1}\left(\cos\frac{5\pi}{6}\right)$	IV. $\frac{\pi}{3}$

Choose the correct answer from the options given below:

Value of cot⁡{π4−2cot⁡−13}\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}cot{4π​−2cot−13} is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Value of $\cot\left\{\frac{\pi}{4} - 2\cot^{-1}3\right\}$ is