Tag: maths

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Questions Related to maths

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

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

  1. $1$
  2. $-1$
  3. $0$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since cos(70 degrees) = sin(20 degrees) and cos(59 degrees) = sin(31 degrees), the first two fractions each equal 1. The term 8 * sin^2(30 degrees) = 8 * (1/2)^2 = 8 * (1/4) = 2. Thus, 1 + 1 - 2 = 0.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a product of the form (4cos^2(x)-1). Using the identity 4cos^2(x)-1 = sin(3x)/sin(x), the product telescopes to sin(3^n * x) / (sin(x) * 2^n). For the given angles, the result is 1.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

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

  1. $2$
  2. $2\sin 20^{o}\csc 40^{o}$
  3. $4$
  4. $4\sin 20^{o}\csc 40^{o}$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rewrite the expression as sqrt(3)/sin(20) - 1/cos(20) = (sqrt(3)cos(20) - sin(20)) / (sin(20)cos(20)). Multiplying numerator and denominator by 2 gives (2 * (sqrt(3)/2 cos(20) - 1/2 sin(20))) / (1/2 * 2 sin(20)cos(20)) = 2 * sin(60 - 20) / (1/2 sin(40)) = 2 * sin(40) / (1/2 sin(40)) = 4.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

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. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice using trigonometric tables trigonometric ratios of some specific angles trigonometric identities trigonometry maths

$ \sqrt { 3 } \ cosec 20 ^ { \circ } - \sec 20 ^ { \circ }$  is equal to :

  1. $2$
  2. $2 \sin 20 ^ { \circ } / \sin 40 ^ { \circ }$
  3. $4$
  4. $4 \sin 20 ^ { \circ } / \sin 40 ^ { \circ }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Expressing csc(20) as 1/sin(20) and sec(20) as 1/cos(20), the expression becomes sqrt(3)/sin(20) - 1/cos(20). Combining terms and using the sine subtraction formula with a factor of 2 yields 4, identical to the standard identity reduction.