Tag: using trigonometric tables

Questions Related to using trigonometric tables

Values of : $sin{ 10 }^{ 0 }sin{ 50 }^{ 0 }sin{ 60 }^{ 0 }sin{ 70 }^{ 0 }$ is

  1. $\cfrac { 3 }{ 16 } $

  2. $\cfrac { 5 }{ 16 } $

  3. $\cfrac { \sqrt { 3 } }{ 16 } $

  4. $\cfrac { \sqrt { 5 } }{ 16 } $


Correct Option: C
Explanation:

As we know that

$\sin A\sin(60^{\circ}-A)\sin (60^{\circ}+A)=\dfrac{1}{4}\sin 3 A$
Put $A=10^{\circ}$
So $\sin 10^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\dfrac{1}{4}\sin 30^{\circ}=\dfrac{1}{8}$
So $\sin 10^{\circ}\sin 60^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\sin 60^{\circ}(\sin 10^{\circ}\sin 50^{\circ}\sin 70^{\circ})=\dfrac{\sqrt{3}}{2}\times \dfrac{1}{8}=\dfrac{\sqrt{3}}{16}$

$sin^21^0+sin^22^0+sin^23^0+....+sin^290^0$

  1. 0

  2. 1

  3. 89/2

  4. 91/2


Correct Option: A

$\frac { cos{ 70 }^{ \circ  } }{ sin{ 20 }^{ \circ  } } +\frac { cos{ 59 }^{ \circ  } }{ sin{ 31 }^{ \circ  } } -8{ sin }^{ 2 }{ 30 }^{ \circ  }$

  1. $1$

  2. $-1$

  3. $0$

  4. $2$


Correct Option: A

The value of $(4 \, cos^2 9^o - 1) (4 cos^2 27^o - 1) (4 \, cos^2 81^o - 1) (4 \, cos^2 243^o - 1) $ is 

  1. 1

  2. -1

  3. 2

  4. none of these


Correct Option: A

$sin{ 40 }^{ \circ  }{ 35 }^{ | }cos{ 19 }^{ \circ  }{ 25 }^{ | }+cos{ 40 }^{ \circ  }{ 35 }^{ | }sin{ 19 }^{ \circ  }{ 25 }^{ |= }$

  1. 1

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

  3. $0$

  4. $-1$


Correct Option: A

$\sqrt {3}\csc 20^{o}-\sec 20^{o}$ is equal to

  1. $2$

  2. $2\sin 20^{o}\csc 40^{o}$

  3. $4$

  4. $4\sin 20^{o}\csc 40^{o}$.


Correct Option: B

$tan{ 40 }^{ \circ  }+tan{ 80 }^{ \circ  }-\sqrt { 3 } tan{ 40 }^{ \circ  }tan{ 80 }^{ \circ  }=$

  1. $\sqrt { 3 } $

  2. $\sqrt { -3 } $

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

  4. $\frac { -1 }{ \sqrt { 3 } }$


Correct Option: A

$\sin^{-1}\left(\sin 100\right)+\cos^{-1}\left(\cos 100\right)+\tan^{-1}\left(\tan 100\right)+\cot^{-1}\left(\cot 100\right)$ equals to 

  1. $100-31\pi$

  2. $100-32\pi$

  3. $200-63\pi$

  4. $200+63\pi$


Correct Option: A

$\dfrac{tan225 cot81cot69}{cot261 + tan21} $ = 

  1. 1

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

  3. $\sqrt{3}$

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


Correct Option: A

Find the value of, $\dfrac {4}{3}\cot^{2}30^{o}+\cot^{2}60^{o}-2\csc ^{2}60^{o}-\dfrac {3}{4}\tan^{2}30^{o}$

  1. $10/3$

  2. $11/3$

  3. $4$

  4. $none\ of\ these$


Correct Option: D
Explanation:

$\dfrac { 4 }{ 3 } { \cot }^{ 2 }30+{ \cot }^{ 2 }60-2{ csc }^{ 2 }60-\dfrac { 3 }{ 4 } { \tan }^{ 2 }30$

$\Rightarrow \dfrac { 4 }{ 3 } { \left( \sqrt { 3 }  \right)  }^{ 2 }+{ \left( \dfrac { 1 }{ \sqrt { 3 }  }  \right)  }^{ 2 }-2\times { \left( \dfrac { 2 }{ \sqrt { 3 }  }  \right)  }^{ 2 }-\dfrac { 3 }{ 4 } \times { \left( \dfrac { 1 }{ \sqrt { 3 }  }  \right)  }^{ 2 }$
$\Rightarrow 4+\dfrac { 1 }{ 3 } -\dfrac { 8 }{ 3 } -\dfrac { 1 }{ 4 } $
$\Rightarrow \dfrac { 15 }{ 4 } -\dfrac { 7 }{ 3 } $
$=\dfrac { 17 }{ 12 } $
None of these.