Tag: trigonometric ratios of some specific angles

Questions Related to trigonometric ratios of some specific angles

The value of ${ cosec }^{ 2 }{ 51 }^{ 0 }-{ cot }^{ 2 }{ 51 }^{ 0 }$ is 

  1. 1

  2. -1

  3. 0

  4. $\frac { 1 }{ 2 } $


Correct Option: A
Explanation:

We know,

$1 + \cot^2\theta = cosec^2 \theta$

$\therefore cosec^2\theta - \cot^2 \theta = 1$

Thus, $cosec^2  51^o - \cot^251^o = 1$

Hence, option a is correct.

Choose the correct option for the following statement.

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

  1. The given statement is true 

  2. The given statement is false

  3. Incomplete information

  4. None of the above.


Correct Option: A
Explanation:

By definition,

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
Therefore, the given statement is true.

$\sin { { 30 }^{ o }= } $

  1. $\dfrac {1}{2}$

  2. $-\dfrac {1}{2}$

  3. $\dfrac {\sqrt {3}}{2}$

  4. $-\dfrac {\sqrt {3}}{2}$


Correct Option: A
Explanation:

As we know that 

$\sin 30^{\circ}=\dfrac{1}{2}$

The value of $\tan 7\dfrac{1}{2}^{o}$ is equal to

  1. $\sqrt{6}+\sqrt{3}+\sqrt{2}-2$

  2. $\sqrt{6}-\sqrt{3}+\sqrt{2}-2$

  3. $\sqrt{6}-\sqrt{3}+\sqrt{2}+2$

  4. $\sqrt{6}-\sqrt{3}-\sqrt{2}-2$


Correct Option: A

General solution of $cotx+tanx=2cosecx$ is

  1. $2n\pi\pm\dfrac{2\pi}{3},n\inZ$

  2. $2n\pi\pm\dfrac{4\pi}{3},n\in Z$

  3. $2n\pi\pm\dfrac{5\pi}{3},n\in Z$

  4. $2n\pi\pm\dfrac{\pi}{3},n\in Z$


Correct Option: A

If $\cos A=\cos $ and $\sin A=\sin B$ then 

  1. $A+B=0$

  2. $A=B$

  3. $A+B=2n \pi$

  4. $A=B+2n \pi$


Correct Option: A

$\left( 1-\dfrac { \cos { 61^{o} }  }{ \cos { 1^{o} }  }  \right) \left( 1-\dfrac { \cos { 62^{o} }  }{ \cos { 2^{o} }  }  \right) \left( 1-\dfrac { \cos { 63^{o} }  }{ \cos { 3^{o} }  }  \right) .......\left( 1-\dfrac { \cos { 119^{o} }  }{ \cos { 59^{o} }  }  \right) $

  1. $-1$

  2. $1$

  3. $2$

  4. $0$


Correct Option: A

If $\tan \theta =\dfrac {\cos 9^{o}+\sin 9^{o}}{\cos 9^{o}-\sin 9^{o}}$, then the value of $\theta$ is

  1. $9^{o}$

  2. $54^{o}$

  3. $18^{o}$

  4. $None\ of\ these$


Correct Option: A

The value of $\tan \theta .\tan (\theta +60^{o})+\tan \theta \tan (\theta -60^{o})+\tan (\theta +60^{o}).\tan (\theta -60^{o})+3$ is  

  1. $0$

  2. $1$

  3. $-1$

  4. $None\ of\ these$


Correct Option: A

The value of $\sin 75^{o}$ is

  1. $\dfrac {2-\sqrt {3}}{\sqrt {2}}$

  2. $\dfrac {\sqrt {3}+1}{2\sqrt {2}}$

  3. $\dfrac {\sqrt {3}-1}{2\sqrt {2}}$

  4. $\dfrac {\sqrt {3}+1}{\sqrt {2}}$


Correct Option: A