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Inverse Trigonometric Functions

15 questions · Mathematics · JEE Advanced

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JEE Advanced
Mathematics
Inverse Trigonometric Functions

Inverse Trigonometric Functions

15 questions · Mathematics · JEE Advanced

The total number of real solutions of the equation $θ = tan^{- 1} (2 tan θ) - \frac{1}{2} sin^{- 1} (\frac{6 t a n θ}{9 + t a n ^{2} θ})$ is (Here, the inverse trigonometric functions $sin^{- 1} x$ and $\tan^{-1}…2025 · Shift 2 · Q19 · MCQ
Considering only the principal values of the inverse trigonometric functions, the value of $tan (sin^{- 1} (\frac{3}{5}) - 2 cos^{- 1} (\frac{2}{5}))$ is2024 · Shift 2 · Q18 · MCQ
Let $tan^{- 1} (x) \in (- \frac{π}{2}, \frac{π}{2})$ , for $x \in R$ . Then the number of real solutions of the equation $1 + cos (2 x) = 2 tan^{- 1} (tan x)$ in the set $(- \frac{3 π}{2}, - \frac{π}{2}) \cup (- \frac{π}{2}, \frac{π}{2}) \cup (\frac{π}{2}, \frac{3 π}{2})$ …2023 · Shift 1 · Q25 · Numerical
For any $y \in R$ , let $cot^{- 1} (y) \in (0, π)$ and $tan^{- 1} (y) \in (- \frac{π}{2}, \frac{π}{2})$ . Then the sum of all the solutions of the equation $tan^{- 1} (\frac{6 y}{9 - y ^{2}}) + cot^{- 1} (\frac{9 - y ^{2}}{6 y}) = \frac{2 π}{3}$ …2023 · Shift 2 · Q20 · MCQ
Considering only the principal values of the inverse trigonometric functions, the value of $\frac{3}{2} cos^{- 1} \frac{2}{2 + π ^{2}} + \frac{1}{4} sin^{- 1} \frac{2 2 π}{2 + π ^{2}} + tan^{- 1} \frac{2}{π}$ is2022 · Shift 1 · Q19 · Numerical
The value of $sec^{- 1} (\frac{1}{4} \sum_{k = 0}^{10} sec (\frac{7 π}{12} + \frac{k π}{2}) sec (\frac{7 π}{12} + \frac{( k + 1 ) π}{2}))$ in the interval $[- \frac{π}{4}, \frac{3 π}{4}]$ …2019 · Shift 2 · Q32 · Numerical
The number of real solutions of the equation $sin^{- 1} (i = 1 \sum \infty x^{i + 1} - x i = 1 \sum \infty (\frac{x}{2})^{i}) = \frac{π}{2} - cos^{1} (i = 1 \sum \infty (\frac{- x}{2})^{i} - i = 1 \sum \infty (- x)^{i})$ …2018 · Shift 1 · Q28 · Numerical
For any positive integer n, define $f_{n} : (0, \infty) \to R$ as $f_{n} = j = 1 \sum n tan^{- 1} (\frac{1}{1 + ( x + j ) ( x + j - 1 )})$ for all x $\in$ (0, $\infty$ ). (Here, the inverse trigonometric…2018 · Shift 2 · Q19 · Multiple correct
If $α$ $= 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9}),$ where the inverse trigonimetric functions take only the principal values, then the correct options(s) is (are)2015 · Shift 2 · Q32 · Multiple correct
Let f : [0, 4 $π$ ] $\to$ [0, $π$ ] be defined by f(x) = cos $-$ 1 (cos x). The number of points x $\in$ [0, 4 $π$ ] satisfying the equation $f (x) = \frac{10 - x}{10}$ is2014 · Shift 1 · Q38 · Numerical
Match List $I$ with List $I I$ and select the correct answer using the code given below the lists: List- $I$ (P.) Let $y (x) = cos (3 cos^{- 1} x), x \in [- 1, 1], x e \pm \frac{3}{2} .$ …2014 · Shift 2 · Q23 · MCQ
The value of $cot (n = 1 \sum 23 cot^{- 1} (1 + k = 1 \sum n 2 k))$ is2013 · Shift 1 · Q31 · MCQ
Match List $I$ with List $I I$ and select the correct answer using the code given below the lists: List $I P .$ $(\frac{1}{y ^{2}} (\frac{c o s ( t a n ^{- 1} y ) + y s i n ( t a n ^{- 1} y )}{c o t ( s i n ^{- 1} y ) + t a n ( s i n ^{- 1} y )})^{2} + y^{4})^{1/2}$ …2013 · Shift 2 · Q29 · MCQ
If $0 < x < 1$ , then $1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{1/2} =$ 2008 · Shift 1 · Q33 · MCQ
Let F(x) be an indefinite integral of $sin^{2} x$ . Statement 1 : The function F(x) satisfies F( $x + π$ ) = F( $x$ ) for all real x. Statement 2 : $sin^{2} (x + π) = sin^{2} x$ for all real x.2007 · Shift 1 · Q35 · MCQ