Inverse Trigonometric Function · Mathematics · NDA

The value of $$\tan \left( {2{{\tan }^{ - 1}}{1 \over 5} - {\pi \over 4}} \right)$$ is

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?

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?

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?

The value of $${\sin ^{ - 1}}\left( {{3 \over 5}} \right) + {\tan ^{ - 1}}\left( {{1 \over 7}} \right)$$ is equal to

The principal value of $${\sin ^{ - 1}}x$$ lies in the interval

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?

What is the value of $$\cos (2{\cos ^{ - 1}}0.8)$$ ?

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 $${\tan ^{ - 1}}(2x) + {\tan ^{ - 1}}(3x) = {\pi \over 4}$$ ?

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?

What is the principal value of $${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$ ?

What is $${\tan ^{ - 1}}\left( {{1 \over 4}} \right) + {\tan ^{ - 1}}\left( {{3 \over 5}} \right)$$ equal to?

What is $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 3}} \right)} \right\}$$ equal to?

What is the value of $${\sin ^{ - 1}}{4 \over 5} + {\sec ^{ - 1}}{5 \over 4} - {\pi \over 2}$$ ?

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?

What is 2 cot $\left(\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right)$ equal to ?

If sec-1 p - cosec-1q = 0, where p > 0, q > 0; then what is the value of p-2 + q-2 ?

What is $1+\sin ^2\left(\cos ^{-1}\left(\frac{3}{\sqrt{17}}\right)\right)$ equal to ?

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?

If 3 sin^-1x + cos^-1x = π, then what is x equal to?

Let sin^-1x + sin^-1y + sin^-1z = $\frac{3\pi}{2}$ for 0 ≤ x, y z ≤ 1. What is the value of x¹⁰⁰⁰ + y¹⁰⁰¹ + z¹⁰⁰²?

What is the value of following?

$\rm cot \left[sin^{-1} \frac{3}{5}+cot^{-1}\frac{3}{2} \right]$

What is the slope of the tangent of y = cos^-1 (cos x) at x = $-\frac{\pi}{4}$?

$\rm tan^{-1}x+cot^{-1}x=\frac{\pi}{2}$ holds, when

The equation $sin^{-1}x-cos^{-1}x=\frac{\pi}{6}$ has