New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Inverse Trigonometric Functions question

2025 · 22 Jan · Shift 1 · Q42

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Inverse Trigonometric Functions
2025 · 22 Jan · Shift 1 · Q42

Inverse Trigonometric Functions question

2025 · 22 Jan · Shift 1 · Q42

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of

16\left(\left(\sec ^{-1} x\right)^2+\left(\operatorname{cosec}^{-1} x\right)^2\right)

is :

A
$24 \pi^2$
B
$18 \pi^2$
C
$22 \pi^2$
D
$31 \pi^2$

More from Inverse Trigonometric Functions

If $\frac{π}{2} \leq x \leq \frac{3 π}{4}$ , then $cos^{- 1} (\frac{12}{13} cos x + \frac{5}{13} sin x)$ is equal to2025 · MCQ
If for some $α, β; α \leq β, α + β = 8$ and $sec^{2} (tan^{- 1} α) + cosec^{2} (cot^{- 1} β) = 36$ , then $α^{2} + β$ is 2025 · Numerical
If $α > β > γ > 0$ , then the expression $cot^{- 1} {β + \frac{( 1 + β ^{2} )}{( α - β )}} + cot^{- 1} {γ + \frac{( 1 + γ ^{2} )}{( β - γ )}} + cot^{- 1} {α + \frac{( 1 + α ^{2} )}{( γ - α )}}$ …2025 · MCQ
$cos (sin^{- 1} \frac{3}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{33}{65})$ is equal to:2025 · MCQ
Let [x] denote the greatest integer less than or equal to x. Then the domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is:2025 · MCQ
Let S = ${x : cos^{- 1} x = π + sin^{- 1} x + sin^{- 1} [2 x + 1]}$ . Then $x \in S \sum (2 x - 1)^{2}$ is equal to .2025 · Numerical
If the domain of the function $sin^{- 1} (\frac{3 x - 22}{2 x - 19}) + lo g_{e} (\frac{3 x ^{2} - 8 x + 5}{x ^{2} - 3 x - 10})$ is $3 α + 10 β$ , then $3 α + 10 β$ is equal to:2024 · MCQ
Given that the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[- 1, 1]$ such that $cos^{- 1} x - sin^{- 1} y = α, \frac{- π}{2} \leq α \leq π$ . Then, the minimum value of $x^{2} + y^{2} + 2 x y sin α$ …2024 · MCQ