Inverse Trigonometric Function · Mathematics · NDA

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MCQ (Single Correct Answer)

1
The value of $$\tan \left( {2{{\tan }^{ - 1}}{1 \over 5} - {\pi \over 4}} \right)$$ is
NDA 2015 Paper 2
2
Consider the following statements

1. $${\sin ^{ - 1}}{4 \over 5} + {\sin ^{ - 1}}{3 \over 5} = {\pi \over 2}$$

2. $${\tan ^{ - 1}}\sqrt 3 + {\tan ^{ - 1}}1 = - {\tan ^{ - 1}}(2 + \sqrt 3 )$$

Which of the above statement(s) is/are correct?
NDA 2015 Paper 2
3
Consider the following statements

1. Theer exists $$\theta \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$ for which $${\tan ^{ - 1}}(\tan \theta ) \ne 0$$.

2. $${\sin ^{ - 1}}\left( {{1 \over 3}} \right) - {\sin ^{ - 1}}\left( {{1 \over 5}} \right)$$

$$ = {\sin ^{ - 1}}\left( {{{2\sqrt 2 (\sqrt 3 - 1)} \over {15}}} \right)$$

Which of the above statements is/are correct?
NDA 2016 Paper 1
4
Consider the following statements

1. $${\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{1 \over x}} \right) = \pi $$

2. Their exist, $$x,y \in [ - 1,1]$$, where x $$\ne$$ y such that $${\sin ^{ - 1}}x + {\cos ^{ - 1}}y = {\pi \over 2}$$.

Which of the above statements is/are correct?
NDA 2016 Paper 1
5
The value of $${\sin ^{ - 1}}\left( {{3 \over 5}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right)$$ is equal to
NDA 2017 Paper 2
6
The principal value of $${\sin ^{ - 1}}x$$ lies in the interval
NDA 2017 Paper 2
7
Let x, y, z be positive real numbers such that x, y, z are in GP and $${\tan ^{ - 1}}x$$, $${\tan ^{ - 1}}y$$ and $${\tan ^{ - 1}}z$$ are in AP. Then which one of the following is correct?
NDA 2017 Paper 1
8
What is the value of $$\cos (2{\cos ^{ - 1}}0.8)$$ ?
NDA 2017 Paper 1
9
Consider the following values of x

1. 8

2. $$-$$4

3. $${1 \over 6}$$

4. $$-$$ $${1 \over 4}$$

Which of the above values of x is/are the solution(s) of the equation $${\tan ^{ - 1}}(2x) + {\tan ^{ - 1}}(3x) = {\pi \over 4}$$ ?
NDA 2018 Paper 2
10
If $$\sin x = {1 \over {\sqrt 5 }}$$, $$\sin y = {1 \over {\sqrt {10} }}$$, where $$0 < x < {\pi \over 2}$$, $$0 < y < {\pi \over 2}$$, then what is (x + y) equal to?
NDA 2018 Paper 1
11
What is the principal value of $${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$ ?
NDA 2018 Paper 1
12
What is $${\tan ^{ - 1}}\left( {{1 \over 4}} \right) + {\tan ^{ - 1}}\left( {{3 \over 5}} \right)$$ equal to?
NDA 2018 Paper 1
13
What is $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 3}} \right)} \right\}$$ equal to?
NDA 2019 Paper 2
14
What is the value of $${\sin ^{ - 1}}{4 \over 5} + {\sec ^{ - 1}}{5 \over 4} - {\pi \over 2}$$ ?
NDA 2019 Paper 1
15
If $${\sin ^{ - 1}}{{2p} \over {1 + {p^2}}} - {\cos ^{ - 1}}{{1 - {q^2}} \over {1 + {q^2}}} = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$, then what is x equal to?
NDA 2019 Paper 1
16

If $\cos^{-1} x = \sin^{-1} x$, then which one of the following is correct?

NDA Mathematics 21 April 2024
17

What is $\sqrt{15 + \cot^2 \left( \frac \pi 4 - 2 \cot^{-1} 3 \right)}$ equal to?

NDA Mathematics 21 April 2024
18

What is $\tan^{-1} \left( \frac{a}{b} \right) - \tan^{-1} \left( \frac{a - b}{a + b} \right)$ equal to?

NDA Mathematics 21 April 2024
19
What is 2 cot $\left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right)$ equal to ?
NDA Mathematics 3 September 2023
20
If sec-1 p - cosec-1q = 0, where p > 0, q > 0; then what is the value of p-2 + q-2 ?
NDA Mathematics 3 September 2023
21
What is $1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to ?
NDA Mathematics 3 September 2023
22
What is tan−1 cot(cosec−1 2) equal to ?
NDA Mathematics 4 September 2022
23
If $\tan^{-1} \left(\frac{1}{2}\right)+\tan^{-1} \left(\frac{x}{3}\right)=\frac{\pi}{4},$ where 0 < x < 6, then what is x equal to?
NDA Mathematics 10 April 2022
24
If 3 sin-1x + cos-1x = π, then what is x equal to?
NDA Mathematics 10 April 2022
25
$\rm tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$ holds, when
NDA Mathematics 18 April 2021
26
The equation $sin^{-1}x-cos^{-1}x=\frac{\pi}{6}$ has
NDA Mathematics 18 April 2021
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