Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

$$\cot^{ -1 } 3 + \cot^{ -1 } 7 + \cot^{ -1 } 13 + n terms =$$

A
$$\tan^{ -1 }\left(\dfrac { n }{ n + 2 }\right)$$

B
$$\tan^{ -1 }\left(\dfrac { n + 2 }{ n }\right)$$

C
$$\tan^{ -1 }\left(\dfrac { 3n }{ 4n + 1 }\right)$$

D
$$\tan^{ -1 }\left(\dfrac { 4n + 1 }{ 3n }\right)$$
Question 2
1 / -0

$$ \sin \cot ^{-1} \tan \cos ^{-1} x $$ is always equal to

A
x

B
$$
\sqrt{1-x^{2}}
$$

C
$$
\frac{1}{x}
$$

D
None of these
Question 3
1 / -0

If $$\theta =\cot ^{ -1 }{ \sqrt { \cos { x } } -\tan ^{ -1 }{ \sqrt { \cos { x } } } } $$, then $$\sin { \theta } =$$

A
$$\tan { \frac { 1 }{ 2 } } x$$

B
$$\tan ^{ 2 }{ \left( \frac { x }{ 2 } \right) } $$

C
$$\frac { 1 }{ 2 } \tan ^{ -1 }{ \left( \frac { x }{ 2 } \right) } $$

D
none of these
Question 4
1 / -0

$$3tan^{ -1 }x\quad =\quad tan^{ -1 }\{ \dfrac { 3x-x^{ 3 } }{ 1-3x^{ 2 } } \} ,\quad then\quad x\quad belong\quad to\quad $$

A
[-1,1]

B
(-1,1)

C
$$\{ -\dfrac { 1 }{ \sqrt { 3 } } ,\dfrac { 1 }{ \sqrt { 3 } } \} $$

D
None of these

Solution
Question 5
1 / -0

If $$\sin^{ -1 }\left(\dfrac { 2a }{ 1 + a^{ 2 } }\right) + \cos^{ -1 }\left(\dfrac { 1-a^{ 2 } }{ 1 + a^{ 2 } }\right) = \tan^{ -1 } \left(\dfrac { 2x }{ 1 x^{ 2 } }\right)$$ where, $$a, x \epsilon \left( 0, 1\right)$$ then the value of $$x$$ is

A
$$0$$

B
$$\dfrac { a }{ 2 }$$

C
$$a$$

D
$$\dfrac { 2a }{ 1 a^{ 2 } }$$
Question 6
1 / -0

If $$\tan^{-1}{\left(\cfrac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)}=\alpha,\left(\alpha\in\left[0,\cfrac{\pi}{4}\right)\right]$$ yhen $$x^2$$ is equal to

A
$$\cos{2\alpha}$$

B
$$\tan{2\alpha}$$

C
$$\sin{2\alpha}$$

D
None of these

Solution
Question 7
1 / -0

Value of $$\sin ^{ -1 }{ \frac { 3 }{ \sqrt { 13 } } +\cos ^{ -1 }{ \frac { 11 }{ \sqrt { 146 } } } +\cot ^{ -1 }{ \sqrt { 3 } } } $$ is

A
$$\pi$$

B
$$\pi$$/2

C
5$$\pi$$/12

D
$$\pi$$/3

Solution
Question 8
1 / -0

The least positive integer n for which $$\left( \frac { 1+i }{ 1-i } \right) ^{ n }=\frac { 2 }{ \pi } \left( \sec ^{ -1 }{ \frac { 1 }{ x } +\sin ^{ -1 }{ x } } \right) \left( where,\quad x\neq 0,-1\le x\ge 1\quad and\quad i=\sqrt { -1 } \right) $$, is

A
2

B
4

C
6

D
8

Solution
Question 9
1 / -0

If $$2sin^{-1}( \frac {3}{5})-cos^{-1}(\frac{5}{13})=cos^{-1} (\lambda)$$, then $$\lambda$$ is eual to

A
323/225

B
223/325

C
323/325

D
123/125

Solution
Question 10
1 / -0

If a is a real of the equation $${ x }^{ 3 }+3x-tan2=0$$ then $${ cot }^{ -1 }a+{ cot }^{ -1 }\dfrac { 1 }{ a } -\dfrac { x }{ 2 } $$ can be equal to

A
0

B
$$\dfrac { \pi }{ 2 } $$

C
$$\pi $$

D
$$\dfrac { 3\pi }{ 2 } $$

Solution