New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Inverse Trigonometric Functions question

2025 · 24 Jan · Shift 1 · Q49

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

PYQ Library
JEE Main
Mathematics
Inverse Trigonometric Functions
2025 · 24 Jan · Shift 1 · Q49

Inverse Trigonometric Functions question

2025 · 24 Jan · Shift 1 · Q49

JEE MainMathematicsInverse Trigonometric FunctionsNumerical+4 / −1

If for some

\alpha, \beta ; \alpha \leq \beta, \alpha+\beta=8

and

\sec ^2\left(\tan ^{-1} \alpha\right)+\operatorname{cosec}^2\left(\cot ^{-1} \beta\right)=36

, then

\alpha^2+\beta

is

\underline{\hspace{2cm}}

Numerical answer

More from Inverse Trigonometric Functions

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
For $n \in N$ , if $cot^{- 1} 3 + cot^{- 1} 4 + cot^{- 1} 5 + cot^{- 1} n = \frac{π}{4}$ , then $n$ is equal to .2024 · Numerical
Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 sin^{- 1} x + 3 cos^{- 1} x = \frac{2 π}{5}$ , is .2024 · Numerical