Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 65

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Question 1
1 / -0

Solution of $${\tan ^{ - 1}}\frac{{2x}}{{1 - {x^2}}} + {\cot ^{ - 1}}\frac{{1 - {x^2}}}{{2x}} = \frac{{2\pi }}{3}\,\,$$ are

A
$$\frac{1}{{\sqrt 3 }}$$

B
$$ - \sqrt 3 $$

C
$$\sqrt 3 + 2$$

D
$$\sqrt 3 - 2$$

Solution
Question 2
1 / -0

If $$A=\tan {-1}(\frac {x\sqrt 3}{2k-x})$$ and $$B=\tan ^{-1}(\frac {2x-k}{k\sqrt 3})$$, then the value of A-B is

A
$$0^o$$

B
$$45^o$$

C
$$60^o$$

D
$$30^o$$
Question 3
1 / -0

If $$\alpha$$ is the only real root of the equation $$\displaystyle x^3 + bx^2 + c = 0 $$ ($$b$$ < $$c$$) then the value of $$\displaystyle Tan^{1}\alpha + Tan^{1}\left ( \dfrac{1}{\alpha} \right ) $$ =

A
$$\dfrac{\pi}{2}$$

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

C
$$0$$

D
$$\pi$$

Solution
Question 4
1 / -0

If $$\displaystyle Sin^{1}(x - \dfrac{x^2}{2} + \dfrac{x^3}{4} - .......) + Cos^{1}(x^2 - \dfrac{x^4}{2} + \dfrac{x^6}{4} - ......) = \dfrac{\pi}{2} $$ for 0 < $$\left | x \right |$$ < $$\sqrt{2}$$ then $$x$$ =

A
1/2

B
1

C
1/2

D
1

Solution
Question 5
1 / -0

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

A
$$0$$

B
$$\cfrac { \pi }{ 4 } $$

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

D
$$\cfrac { \pi }{ 2 } $$

Solution
Question 6
1 / -0

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

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

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

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

D
$$\pi $$
Question 7
1 / -0

If $$A=\tan ^{-1}(\frac {x\sqrt 3}{2k-x})$$ and $$B=\tan {-1}(\frac {2x-k}{k\sqrt 3})$$, then the value of $$A-B$$ is

A
$$0^o$$

B
$$45^o$$

C
$$60^o$$

D
$$30^o$$

Solution
Question 8
1 / -0

If $$x$$ = $$Tan^{1}(1)$$ + $$Cos^{1}(\dfrac{1}{2})$$ + $$Sin^{1}(\dfrac{1}{2})$$ and $$y$$ = $$ cos\left [ \dfrac{1}{2}Cos^{1}(1/8) \right ] $$ then

A
$$x$$ = $$2\, \pi\, y$$

B
$$y$$ = $$3\, \pi\, x$$

C
$$x$$ = $$\pi\, y$$

D
$$y$$ = $$\pi\, x$$

Solution
Question 9
1 / -0

If $$A=2{\tan}^{-1}\left(2\sqrt{2}-1\right)$$ and $$B=3{\sin}^{-1}\left(1/3\right)+{sin}^{-1}\left(3/5\right)$$, then

A
$$A=B$$

B
$$A<B$$

C
$$A>B$$

D
$$none \of \these$$

Solution
Question 10
1 / -0

The value of $${\sin}^{-1}\left( \sin12 \right )+{\sin}^{-1}\left( \cos12 \right )=$$

A
$$0$$

B
$$24-2\pi$$

C
$$4\pi-24$$

D
$$8\pi$$