The value of (1/2^(-1)(5)/3) is equal to Option 1: (5-3)/2 Option 2: (5+3)/2 Option 3: (3+5)/2 Option 4: (3-5)/2

Answer: (3-5)/2. Solution: Let =^(-1)√5/3, so =√5/3 and =√(1-5/9)=2/3. Using ()/2=(1-)/(), the value is (1-√5/3)/(2/3)=(3-√5)/2.

Geometry

Trigonometry

Medium

core

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to

$\dfrac{5-\sqrt3}{2}$

$\dfrac{5+\sqrt3}{2}$

$\dfrac{3+\sqrt5}{2}$

$\dfrac{3-\sqrt5}{2}$

✅ Correct Option: 4

Let $\theta=\cos^{-1}\frac{\sqrt{5}}{3}$ , so $\cos\theta=\frac{\sqrt{5}}{3}$ and $\sin\theta=\sqrt{1-\frac{5}{9}}=\frac{2}{3}$ . Using $\tan\frac{\theta}{2}=\frac{1-\cos\theta}{\sin\theta}$ , the value is $\frac{1-\frac{\sqrt{5}}{3}}{\frac{2}{3}}=\frac{3-\sqrt{5}}{2}$ .

2026: 22 May Shift 1

Match List-I with List-II

List-I (Function)	List-II (Principal value of y)
(A) $y=\sin^{-1}\left(-\frac{1}{2}\right)$	(I) $\frac{3\pi}{4}$
(B) $y=\cot^{-1}\left(-\frac{1}{\sqrt3}\right)$	(II) $-\frac{\pi}{4}$
(C) $y=cosec^{-1}(-\sqrt2)$	(III) $-\frac{\pi}{6}$
(D) $y=\cos^{-1}\left(-\frac{1}{\sqrt2}\right)$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

2023: 30 May Shift 3

Let $a \leq \tan^{-1} x + \cot^{-1} x + \sin^{-1} x \leq b$ . If $\alpha$ and $\beta$ denote the minimum and maximum possible values of a and b respectively, then :

2026: 21 May Shift 1

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

2025: 26 May Shift 2

Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

2026: 29 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	If $\cos^{-1}\alpha + \cos^{-1}\beta + \cos^{-1}\gamma = 3\pi$ then $\alpha(2\beta+\gamma) + \beta(2\gamma+\alpha) + \gamma(2\alpha+\beta)$ equals	I.	$1$
B.	The value of $\tan^2(\sec^{-1}4) + \cot^2(\text{cosec}^{-1}5)$ is	II.	$9$
C.	If $\sin\left(\cos^{-1}\dfrac{2}{5} + \sin^{-1}x\right) = 1$ then $10x$ equals	III.	$4$
D.	The length of the interval of domain of $\sin^{-1}2x$ is	IV.	$39$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) Range of $y = \text{cosec}^{-1}x$	(I) $R - (-1, 1)$
(B) Domain of $\sec^{-1}x$	(II) $(0, \pi)$
(C) Domain of $\sin^{-1}x$	(III) $[-1, 1]$
(D) Range of $y = \cot^{-1}x$	(IV) $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] - \{0\}$

Choose the correct answer from the options given below :

The value of tan⁡(12cos⁡−153)\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)tan(21​cos−135​​) is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\tan\left(\dfrac{1}{2}\cos^{-1}\dfrac{\sqrt5}{3}\right)$ is equal to