Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 67

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Weekly Quiz Competition

Question 1
1 / -0

the number o real soluttion of $${ tan }^{ -1 }\sqrt { x(x+1) } +{ sin }^{ -1 }\sqrt { { x }^{ 2 }+x+1 } =\frac { \pi }{ 2 } is$$

A
zero

B
one

C
two

D
infinit

Solution
Question 2
1 / -0

The numerical value of $$cot\left( { 2sin }^{ -1 }\dfrac { 3 }{ 5 } +{ cos }^{ -1 }\dfrac { 3 }{ 5 } \right) $$ is

A
$$\dfrac { -4 }{ 3 } $$

B
$$\dfrac { -3 }{ 4 } $$

C
$$\dfrac { 3 }{ 4 } $$

D
$$\dfrac { 4 }{ 3 } $$

Solution
Question 3
1 / -0

If $${ sin }^{ -1 }\left( \dfrac { \sqrt { x } }{ 2 } \right) +{ sin }^{ -1 }\left( \sqrt { 1-\dfrac { x }{ 4 } } \right) +tan^{ -1 }y=\dfrac { 2\pi }{ 3 } $$ then

A
maximum value of $${ x }^{ 2 }+{ y }^{ 2 }$$ is $$\dfrac { 49 }{ 3 } $$

B
maximum value of $${ x }^{ 2 }+{ y }^{ 2 }$$ is 4

C
maximum value of $${ x }^{ 2 }+{ y }^{ 2 }$$ is $$\quad \dfrac { 1 }{ 2 } $$

D
maximum value of $${ x }^{ 2 }+{ y }^{ 2 }$$ is 3
Question 4
1 / -0

$${ cos }^{ -1 }\left[ 2cot^{ -1 }\left( \surd 2-1 \right) \right] $$ is equal to

A
$$\sqrt { 2 } -1$$

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

C
$$\pi /4$$

D
$$3\pi /4$$

Solution
Question 5
1 / -0

If $${ \cot }^{ -1 }(\sqrt { \cos a } )-{ \tan }^{ -1 }(\sqrt { \cos a } )=x,$$ then $$\sin x$$ is equal to

A
$${ \cot }\dfrac { a }{ 2 } $$

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

C
$${\tan }^{ 2 }\dfrac { a }{ 2 } \quad $$

D
$$\tan a$$

Solution
Question 6
1 / -0

$${ tan }^{ -1 }\left( \dfrac { \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1+{ -x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1{ -x }^{ 2 } } } \right) ,[x]\le \dfrac { 1 }{ \sqrt { 2 } } ,is\quad equal\quad to$$

A
$$\dfrac { 1 }{ 2 } { cos }^{ -1 }{ x }^{ 2 }$$

B
$$\frac { \pi }{ 4 } -\dfrac { 1 }{ 2 } { cos }^{ -1 }{ x }^{ 2 }$$

C
$$\frac { \pi }{ 4 } +\dfrac { 1 }{ 2 } { cos }^{ -1 }{ x }^{ 2 }$$

D
$$\frac { \pi }{ 2 } -\dfrac { 1 }{ 2 } { cos }^{ -1 }{ x }^{ 2 }$$

Solution
Question 7
1 / -0

If If $$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = r ^ { 2 } ,$$ then $$tan^ { - 1 } \left( \frac { x y } { z r } \right) + \tan ^ { - 1 } \left( \frac { y z } { x r } \right) + \tan ^ { - 1 } \left( \frac { x z } { y r } \right)$$ =

A
$$\pi$$

B
$$\frac { \pi } { 2 }$$

C
0

D
none of these.

Solution
Question 8
1 / -0

If $$cos^{-1}x - cos^{-1}\dfrac{y}{2} = \alpha$$ , then $$4x^2 - 4xy\, cos\, \alpha + y^2$$ is equal to -

A
$$2\, sin\, 2\alpha$$

B
$$4$$

C
$$4\, sin^2\alpha$$

D
$$-4\, sin^2\alpha$$
Question 9
1 / -0

If $$\cos ^ { - 1 } ( x / a ) + \cos ^ { - 1 } ( y / b ) = \alpha ,$$ Then $$x ^ { 2 } / a ^ { 2 } + y ^ { 2 } / b ^ { 2 }$$ is equal to:

A
$$( 2 x y / a b ) \cos \alpha + \sin ^ { 2 } \alpha$$

B
$$( 2 x y / a b ) \sin \alpha + \cos ^ { 2 } \alpha$$

C
$$( 2 x y / a b ) \cos ^ { 2 } \alpha + \sin \alpha$$

D
$$( 2 x y / a b ) \sin ^ { 2 } \alpha + \cos \alpha$$

Solution
Question 10
1 / -0

If $$sin^{-1}x+sin^{-1}y=\cfrac {2 \pi}3$$, then cos^{-1}x+cos^{-1}y$$ equal to

A
$$\cfrac {2 \pi} 3$$

B
$$\cfrac {\pi}3$$

C
$$\cfrac {\pi}6$$

D
$$\pi$$