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

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. $\sqrt{6}-\sqrt{3}-\sqrt{2}-2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula tan(x/2) = sqrt((1-cos x)/(1+cos x)) with x = 15 degrees, or using the half-angle identity for 7.5 degrees, the value is sqrt(6) + sqrt(3) + sqrt(2) - 2.

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

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. $2n\pi\pm\dfrac{\pi}{3},n\in Z$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rewrite the equation cot(x) + tan(x) = 2 csc(x) in terms of sine and cosine: (cos(x)/sin(x)) + (sin(x)/cos(x)) = 2 / sin(x). Simplifying the left side gives 1 / (sin(x)cos(x)) = 2 / sin(x), which leads to cos(x) = 1/2 for sin(x) not equal to 0. Solving cos(x) = 1/2 yields x = 2n pi plus or minus pi/3.

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

$\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. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a telescoping product. Each term (1 - cos(60+x)/cos(x)) simplifies to (cos x - cos(60+x))/cos x = (2 sin(60/2 + x) sin(60/2))/cos x. The product eventually cancels out to -1.

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

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. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Divide numerator and denominator by cos(9 degrees) to get tan(theta) = (1 + tan(9 degrees)) / (1 - tan(9 degrees)) = tan(45 degrees + 9 degrees) = tan(54 degrees). Thus, theta = 54 degrees.

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

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. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the identity tan(A)tan(B)tan(C) = tan(A+B+C) - (tan A + tan B + tan C) or expanding the terms, the expression simplifies to 0.

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

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. $\dfrac {\sqrt {3}+1}{\sqrt {2}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Express sin(75 degrees) as sin(45 degrees + 30 degrees). Using the sine addition formula, sin(45)cos(30) + cos(45)sin(30) = (1/sqrt(2))(sqrt(3)/2) + (1/sqrt(2))(1/2) = (sqrt(3) + 1) / (2 * sqrt(2)).