### Mathematics - Inverse Trigonometric Functions

#### Question - 1

The value of sin $\left[ \frac { \pi }{ 2 } -{ sin }^{ -1 }\left( -\frac { 1 }{ 2 } \right) \right]$ is

• A $\frac { \sqrt { 3 } }{ 4 }$
• B $\frac { \sqrt { 3 } }{ 2 }$
• C $-\frac { \sqrt { 3 } }{ 2 }$
• D $-\sqrt { 3 }$

#### Question - 2

Find the value of $sin\left\{ \left( \frac { \pi }{ 2 } -{ sin }^{ -1 }\left( -\frac { \sqrt { 3 } }{ 2 } \right) \right) \right\}$

• A $\frac { 1 }{ 3 }$
• B $\frac { 1 }{ 2 }$
• C $-\frac { 1 }{ 2 }$
• D $\frac { 2 }{ 3 }$

#### Question - 3

The value of ${ sin }^{ -1 }\left\{ cos\left( \frac { 43\pi }{ 5 } \right) \right\}$ is

• A $\frac { 3\pi }{ 5 }$
• B $\frac { -7\pi }{ 5 }$
• C $\frac { \pi }{ 10 }$
• D $-\frac { \pi }{ 10 }$

#### Question - 4

The angle ${ tan }^{ -1 }\left( tan\frac { 3\pi }{ 4 } \right)$ is

• A $\frac { \pi }{ 2 }$
• B $-\frac { \pi }{ 3 }$
• C $-\frac { \pi }{ 4 }$
• D $\frac { \pi }{ 4 }$

#### Question - 5

If ${ tan }^{ -1 }x=\frac { \pi }{ 10 }$ for some $x\epsilon R$, then the value of cot-1 x is

• A $\frac { \pi }{ 5 }$
• B $\frac { 2\pi }{ 5 }$
• C $\frac { 3\pi }{ 5 }$
• D $\frac { 4\pi }{ 5 }$

#### Question - 6

The value of cos $\left( { tan }^{ -1 }\frac { 3 }{ 4 } \right)$ is

• A $\frac { 3 }{ 2 }$
• B $\frac { 1 }{ 2 }$
• C $\frac { 4 }{ 5 }$
• D $-\frac { 1 }{ 2 }$

#### Question - 7

The range of $f(x)=\left| { 3tan }^{ -1 }x-{ cos }^{ -1 }(0) \right| { -cos }^{ -1 }(-1)$ is

• A $[-\pi ,\pi )$
• B $(-\pi ,\pi )$
• C $[-\pi ,\pi ]$
• D $\left[ -\frac { \pi }{ 2 } ,\frac { \pi }{ 2 } \right)$

#### Question - 8

The number of solutions of the equation cos ( cos-1 x) = cosec (cosec-1 x) is

• A 2
• B 3
• C 4
• D 1

#### Question - 9

${ tan }^{ -1 }\sqrt { 3 } -{ cot }^{ -1 }(-\sqrt { 3 } )$ is equal to

• A $\pi$
• B $-\frac { \pi }{ 2 }$
• C zero
• D $2\sqrt { 3 }$

#### Question - 10

The value of cos (2cos-1 x + sin-1 x) at $x=\frac { 1 }{ 5 }$ is

• A 1
• B 3
• C 0
• D $-\frac { 2\sqrt { 6 } }{ 5 }$