The maximum value of x + x, x R is: Option 1: 2 Option 2: √2 Option 3: 1/√2 Option 4: Not known

Answer: √2. Solution: x + x = √2(x + /4). Since has maximum value 1, the maximum of the expression is √2.

Geometry

Trigonometry

Easy

core

The maximum value of $\sin x + \cos x, x \in R$ is:

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

Not known

✅ Correct Option: 2

$\sin x + \cos x = \sqrt{2}\sin(x + \pi/4)$ . Since $\sin$ has maximum value 1, the maximum of the expression is $\sqrt{2}$ .

2022: 16 July Shift 2

The value of $\text{cosec}^{-1}(-2) - 2\sec^{-1}(-2)$ is equal to:

2025: 22 May Shift 1

The minimum value of the function $f(x) = 3\sin x - 4\cos x, x \in [-4\pi, 4\pi]$ is equal to

2023: 30 May Shift 3

The maximum value of $(\sin x)(\cos x)$ is :

2026: 18 May Shift 2

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

2025: 19 May Shift 1

The maximum value of $\sin x \cdot \cos x$ 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: