Inverse Trigonometric Functions, Solved Paper Question: Jee 1 year MATH, Math

All x satisfying the inequality (cot⁻¹ x)² − 7 (cot⁻¹ x) + 10 > 0, lie in the interval:

JEE Mains 2019

If x = sin^–1(sin10) and y = cos^–1(cos10), then y – x is equal to:

JEE Mains 2019

Considering only the principal values of inverse functions, the set

A = \{x \geq 0 : \tan^{- 1} (2 x) + \tan^{- 1} (3 x) = \frac{π}{4}\}

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JEE Mains 2019

If

\cos^{- 1} (\frac{2}{3 x}) + \cos^{- 1} (\frac{3}{4 x}) = \frac{π}{2} (x > \frac{3}{4}),

then x is equal to:

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JEE Mains 2019

If an angle between the line,

\frac{x + 1}{2} = \frac{y - 2}{1} = \frac{z - 3}{- 2}

and the plane,

x - 2 y - k z = 3 is \cos^{- 1} (\frac{2 \sqrt{2}}{3})

, then a value of k is :

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JEE Mains 2019

The number of real solutions of the equation

\sin^{- 1} (\sum_{i = 1}^{\infty} x^{i + 1} - x \sum_{i = 1}^{\infty} {(\frac{x}{2})}^{i}) = \frac{π}{2} - \cos^{- 1} (\sum_{i = 1}^{\infty} {(- \frac{x}{2})}^{i} - x \sum_{i = 1}^{\infty} {(- x)}^{i})

lying in the interval

(- \frac{1}{2}, \frac{1}{2})

is _____ .
(Here, the inverse trigonometric functions sin⁻¹𝑥 and cos⁻¹𝑥 assume values in [

- \frac{π}{2}, \frac{π}{2}

] and [0, 𝜋], respectively.)

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JEE Advanced 2018

For any positive integer n, define f_n : (0, ∞) → ℝ as

f_{n} (x) = \sum_{j = 1}^{n} \tan^{- 1} (\frac{1}{1 + (x + j) (x + j - 1)})

for all x ∈ (0, ∞).

(Here, the inverse trigonometric function \tan^{- 1} x assumes values in (- \frac{π}{2}, \frac{π}{2}) .)

Then, which of the following statement(s) is (are) TRUE?

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JEE Advanced 2018

If

α = 3 \sin^{- 1} (\frac{6}{11}) and β = 3 \cos^{- 1} (\frac{4}{9})

, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)

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JEE Advanced 2015

Let

\tan^{- 1} y = \tan^{- 1} x + \tan^{- 1} (\frac{2 x}{1 - x^{2}}),

where

|x| < \frac{1}{\sqrt{3}}

. Then a value of y is:

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JEE Mains 2015

Let

f : [0, 4 π] \to [0, π]

be defined by f(x) = cos⁻¹ (cos x). The number of points x ∈

[0, 4 π]

satisfying the equation

f (x) = \frac{10 - x}{10}

is

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JEE Advanced 2014

The value of cot is

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JEE Advanced 2013

If x, y, z are in A.P. and tan⁻¹x, tan⁻¹y, and tan⁻¹z, are also in A.P., then :

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JEE Mains 2013

Match List I with List II and select the correct answer using the code given below the lists:

	List I		List II
P.		1.
Q.	possible value of is	2.
R.		3.
S.	then possible value of x is	4.	1

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JEE Advanced 2013

If 0 < x < 1, then is equal to

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JEE 2008

Let (x, y) be such that
sin⁻¹(ax) + cos⁻¹(y) + cos⁻¹(bxy) =

\frac{π}{2} .

Match the statements in Column I with the statements in Column II and mark your answer in the 4 × 4 matrix given in the ORS.

Column I		Column II
(A)	If a = 1 and b = 0, then (x, y)	(p)	lies on the circle x² + y² = 1
(B)	If a = 1 and b = 1, then (x, y)	(q)	lies on (x² − 1) (y² − 1) = 0
(C)	If a = 1 and b = 2, then (x, y)	(r)	lies on y = x
(D)	If a = 2 and b = 2, then (x, y)	(s)	lies on (4x² − 1) (y² − 1) = 0

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JEE 2007

Let

f : [- 1, 1] \to R

,

f^{'} (0) = \lim_{n \to \infty} n f (\frac{1}{n})

and f (0) = 0. Find the value of

\lim_{n \to \infty} \frac{2}{π} (n + 1) \cos^{- 1} (\frac{1}{n}) - n

; given that

0 < |\lim_{n \to \infty} \cos^{- 1} (\frac{1}{n})| < \frac{π}{2} .

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JEE 2004

Prove that cos tan^-1 sin $\cot^{-1} x = \sqrt{\frac{x^{2} +1}{x^{2} +2}}$ .

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JEE 2002