Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 63

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Weekly Quiz Competition

Question 1
1 / -0

If $$\sin^{-1} x+\sin^{-1} y=\dfrac{\pi}{3}$$ then the value of $$\cos^{-1}x+\cos^{-1}y$$ is equal to which of the following :

A
$$\dfrac{\pi}{6}$$

B
$$\dfrac{\pi}{3}$$

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

D
$$\pi$$

Solution
Question 2
1 / -0

$$ \tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)=\dots $$

A
$$ \frac{\pi}{2} $$

B
$$ \frac{\pi}{3} $$

C
$$ \frac{\pi}{2} $$

D
$$ \frac{\pi}{4} $$ or $$ \frac{3 \pi}{4} $$

Solution
Question 3
1 / -0

$$f ( x ) = \sin ^ { - 1 } \sqrt { \frac { \sqrt { 1 + x ^ { 2 } } - 1 } { 2 \sqrt { 1 + x ^ { 2 } } } } ,$$ then which of the following is (are) correct?

A
$$f ( -1 ) = \frac { - 1 } { 4 }$$

B
$$\operatorname { Ran } \mathscr { f } _ { f ( x ) }$ is $\left[ 0 , \frac { \pi } { 2 } \right]$$

C
$$f ^ { \prime } ( x )$$ is an odd function

D
$$\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x } = \frac { 1 } { 2 }$$

Solution
Question 4
1 / -0

If $$x = {\sin ^{ - 1}}\left( {\sin 10} \right)\,\,and\,\,y = {\cos ^{ - 1}}\left( {\cos 10} \right),\,\,then\,\,y - x$$ is equal to:

A
$$\pi $$

B
$$0$$

C
$$7\pi $$

D
$$10$$

Solution
Question 5
1 / -0

If for $$x < -1,\ cos^{-1}{\left(\dfrac{x^{2}-1}{x^{2}+1}\right)}+sin^{-1}{\left(\dfrac{2x}{1+x^{2}}\right)}-tan^{-1}{\left(\dfrac{2x}{x^{2}-1}\right)}=\dfrac{\pi}{3}$$, then $$x=$$

A
$$-\sqrt{3}$$

B
$$-\sqrt{2}$$

C
$$-2$$

D
$$-2\sqrt{3}$$

Solution
Question 6
1 / -0

Solve $${ \tan }^{ -1 }\left(\cfrac { \cos x }{ 1+\sin x }\right) $$.

A
$$ \dfrac { \pi }{ 4 } + \dfrac { x }{ 2 } $$

B
$$ \dfrac { \pi }{ 4 } - \dfrac { x }{ 2 } $$

C
$$ \dfrac { \pi }{ 4 } + { x }$$

D
$$ \dfrac { \pi }{ 4 } - { x } $$

Solution
Question 7
1 / -0

If $${ cos }^{ -1 }\sqrt { p } +{ cos }^{ -1 }\sqrt { 1-p } +{ cos }^{ -1 }\sqrt { 1-q } =\frac { 3\pi }{ 4 } $$ then the value of q is equal to:

A
1

B
$$\dfrac { 1 }{ \sqrt { 2 } } $$

C
$$\dfrac { 1 }{ 3 } $$

D
$$\dfrac { 1 }{ 2 } $$
Question 8
1 / -0

The value of $$\sin ^{-1}[\cot{(\sin ^{-1}\sqrt{(\frac{2 - \sqrt 3}{4})} + \cos ^{-1}\frac{\sqrt {12}}{4})} + \sec ^{-1}\sqrt 2]$$

A
0

B
$$\frac{\pi}{4}$$

C
$$\frac{\pi}{6}$$

D
$$\frac{\pi}{2}$$
Question 9
1 / -0

The solution set of the equation $${ sin }^{ -1 }\sqrt { 1-{ x }^{ 2 } } +{ cos }^{ -1 }x={ cot }^{ -1 }\left( \frac { \sqrt { 1-{ x }^{ 2 } } }{ x } \right) -{ sin }^{ -1 }x$$ is

A
[-1,1] - {0}

B
(0,1] U {-1]

C
[-1,0) U {1}

D
[-1,1]

Solution
Question 10
1 / -0

Number of solutions of the equation
$$tan^{ -1 } \left( \dfrac { 1 }{ a-1 }\right) = tan^{ -1 } \left(\dfrac { 1 }{ x }\right) + tan^{ -1 } \left( \dfrac { 1 }{ a^{ 2 } x + 1}\right)$$

A
$$one$$

B
$$Two$$

C
$$Three$$

D
$$Zero$$

Solution