Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

$$\sum^ { \infty }_ { n=1 } tan^{-1}\dfrac{4n}{n^4-2n^2+2}$$ is equal to:

A
$$tan^{-1}2+tan^{-1}3$$

B
$$4 tan^{-1}1$$

C
$$\pi/2$$

D
$$sec^{-1}(-\sqrt2)$$

Solution
Question 2
1 / -0

$${ cos }^{ -1 }(\frac { x }{ 3 } )+{ cos }^{ -1 }(\frac { y }{ 2 } )=(\frac { \theta }{ 2 } )$$ , then the value of $${ 4x }^{ 2 }$$-12xy cos$$(\frac { \theta }{ 2 } )$$+$${ 9y }^{ 2 }$$ is equal to

A
$$18(1+cos\theta )$$

B
$$18(1-cos\theta )$$

C
$$36(1+cos\theta )$$

D
$$36(1-cos\theta )$$

Solution
Question 3
1 / -0

$$\cos ^{ -1 }{ \left\{ \dfrac { 1 }{ 2 } { x }^{ 2 }+\sqrt { { 1-x }^{ 2 } } .\sqrt { 1\dfrac { { x }^{ 2 } }{ 4 } } \right\} } =\cos ^{ -1 }{ \dfrac { x }{ 2 } } -\cos ^{ -1 }{ x } $$ holds for

A
$$\left| x \right| \le 1$$

B
$$x\in R$$

C
$$0\le x\le 1$$

D
$$-1\le x\le 0$$

Solution
Question 4
1 / -0

$$tan^{-1}y=tan^{-1}x+tan^{-1}(\frac{2x}{1-x^{2}})$$ where $$|x| < \frac{1}{\sqrt{3}}$$. Then a value of y is:

A
$$\dfrac{3x+x^{3}}{1+3x^{2}}$$

B
$$\dfrac{3x-x^{3}}{1+3x^{2}}$$

C
$$\dfrac{3x+x^{3}}{1-3x^{2}}$$

D
$$\dfrac{3x-x^{3}}{1-3x^{2}}$$

Solution
Question 5
1 / -0

$${ tanh }^{ -1 }\left( \frac { 1 }{ 3 } \right) +{ coth }^{ -1 }\left( 3 \right) =.....$$

A
log 2

B
log 3

C
log$$\sqrt { 3 } $$

D
$$log \sqrt { 2 } $$

Solution
Question 6
1 / -0

If $$x=si{ n }^{ -1 }(sin10)$$ and $$y={ s }^{ -1 }(cos10)$$ then $$y-x$$ is equal to:

A
0

B
$$7\pi $$

C
10

D
$$\pi $$

Solution
Question 7
1 / -0

$$\cos ^{ -1 }{ \left( \cos { \dfrac { 7\pi }{ 6 } } \right) } $$ is equal to

A
$$\dfrac {7\pi}{6}$$

B
$$\dfrac {5\pi}{6}$$

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

D
$$\dfrac {\pi}{6}$$

Solution
Question 8
1 / -0

Evaluate $$\cot ^{ -1 }{ \sum _{ n=1 }^{ 19 }{ \cot ^{ -1 }{ [1+\sum _{ p=1 }^{ n }{ 2p } ] } } } $$

A
$$\frac { 23 }{ 22 } $$

B
$$\frac { 19 }{ 23 } $$

C
$$\frac { 23 }{ 19 } $$

D
$$\frac { 22 }{ 23 } $$
Question 9
1 / -0

If $$x={ sin }^{ -1 }(sin10)$$ and $$y={ cos }^{ -1 }(cos10)$$, then the value of (y - x) is

A
$$\pi $$

B
$$7\pi $$

C
0

D
10
Question 10
1 / -0

The value of $$\sin^{-1}(\sin 3)+\cos^{-1}(\cos 7)-\tan^{-1}(\tan 5)$$ is

A
$$\pi-1$$

B
$$\pi$$

C
$$3\pi-1$$

D
$$2\pi-1$$

Solution