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SSC CGL Tier II level Question Set 7, Trigonometry 1

Trigonometry Questions for SSC CGL Tier II Set 7

7th Set of Trigonometry Questions for SSC CGL Tier II with answers

Solve 10 trigonometry questions for SSC CGL Tier II Set 7 in 12 mins by innovative trigonometry problem solving techniques. Verify result from answers.

Answers and link to the solutions are at the end.

Before taking the test it is recommended that you refer to

Tutorial on Basic and rich concepts in Trigonometry and its applications.

Tutorial on Basic and rich concepts in Trigonometry Part 2, Compound angle functions.

Trigonometry concepts part 3, maxima (or minima) of Trigonometric expressions

Basic and rich algebraic concepts for elegant solutions of SSC CGL problems.

Now set the stopwatch alarm and start taking this test.


Trigonometry questions for SSC CGL Tier II Set 7 - testing time 12 mins

Problem 1.

If $x=rsin\alpha {cos\beta}$, $y=rsin\alpha{sin\beta}$ and $z=rcos\alpha$, then,

  1. $x^2-y^2+z^2=r^2$
  2. $x^2+y^2+z^2=r^2$
  3. $x^2+y^2-z^2=r^2$
  4. $y^2+z^2-x^2=r^2$

Problem 2.

With $\angle \theta$ acute, the value of the expression, $\left(\displaystyle\frac{5\ cos \theta - 4}{3-5\ sin \theta} - \displaystyle\frac{3+5\ sin \theta}{4+5\ cos \theta}\right)$ is,

  1. $1$
  2. $0$
  3. $\displaystyle\frac{1}{2}$
  4. $\displaystyle\frac{1}{4}$

Problem 3.

If $4+ 3\ tan \alpha=0$, where $\displaystyle\frac{\pi}{2} \lt \alpha \lt \pi$, the value of $2\ cot \alpha - 5\ cos \alpha + \sin \alpha$ is,

  1. $\displaystyle\frac{23}{10}$
  2. $-\displaystyle\frac{53}{10}$
  3. $\displaystyle\frac{37}{10}$
  4. $\displaystyle\frac{7}{10}$

Problem 4.

If $\ sin \theta + \ sin^2 \theta=1$, then which of the following is true?

  1. $\ cos \theta +\ cos^2 \theta=1$
  2. $\ cos^2 \theta +\ cos^3 \theta=1$
  3. $\ cos^2 \theta +\ cos^4 \theta=1$
  4. $\ cos \theta -\ cos^2 \theta=1$

Problem 5.

If $a=\sec \theta+\tan \theta$, then $\displaystyle\frac{a^2-1}{a^2+1}$ is,

  1. $\sec \theta$
  2. $\cos \theta$
  3. $\tan \theta$
  4. $\sin \theta$

Problem 6.

The value of $\displaystyle\frac{cot \theta + cosec \theta - 1}{cot \theta -cosec \theta +1}$ is,

  1. $cosec \theta - cot \theta$
  2. $cosec \theta + cot \theta$
  3. $sec \theta + cot \theta$
  4. $cosec \theta + tan \theta$

Problem 7.

If $\displaystyle\frac{sin \theta + cos \theta}{sin \theta - cos \theta}=3$, then the value of $sin^4 \theta -cos^4 \theta$ is,

  1. $\displaystyle\frac{2}{5}$
  2. $\displaystyle\frac{1}{5}$
  3. $\displaystyle\frac{4}{5}$
  4. $\displaystyle\frac{3}{5}$

Problem 8.

If $asec \theta+btan \theta +c=0$, and $psec \theta +qtan \theta +r=0$, then the value of $(br-qc)^2-(pc-ar)^2$ is,

  1. $(aq+bp)^3$
  2. $(aq-bp)^3$
  3. $(aq+bp)^2$
  4. $(aq-bp)^2$

Problem 9.

If $\alpha + \beta + \gamma=\pi$, then the value of $(sin^2 \alpha + sin^2 \beta - sin^2 \gamma)$ is,

  1. $2sin \alpha{sin \beta}cos \gamma$
  2. $2sin \alpha$
  3. $2sin \alpha{cos \beta}sin \gamma$
  4. $2sin \alpha{sin \beta}sin \gamma$

Problem 10.

If $sin\alpha sin\beta-cos\alpha cos\beta + 1=0$, then the value of $cot\alpha tan\beta$ is,

  1. $-1$
  2. $1$
  3. $0$
  4. None of these

The answers are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL Tier II level Solution Set 7 on Trigonometry 1.


Answers to the Trigonometry Questions for SSC CGL Tier II Set 7

Problem 1. Answer: b: $x^2+y^2+z^2=r^2$.

Problem 2. Answer: b: 0.

Problem 3. Answer: a: $\displaystyle\frac{23}{10}$.

Problem 4. Answer: c: $cos^2\theta + cos^4\theta=1$

Problem 5. Answer: d: $sin \theta$.

Problem 6. Answer: b: $cosec \theta + cot \theta$.

Problem 7. Answer: d: 1.

Problem 8. Answer: d: $(aq-bp)^2$.

Problem 9. Answer: a: $2sin\alpha sin\beta cos \gamma$.

Problem 10. Answer: a: $-1$.


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