SSC CGL Tier II level Question Set 7, Trigonometry 1 | SureSolv

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SSC CGL Tier II level Question Set 7, Trigonometry 1

7th SSC CGL Tier II level Question Set, topic Trigonometry 1

SSC CGL Tier 2 question set 7 trigonometry1

This is the 7th question set of 10 practice problem exercise for SSC CGL Tier II level exam and 1st on topic Trigonometry.

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.


7th question set- 10 problems for SSC CGL Tier II exam: 1st on Trigonometry - testing time 15 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.

If you wish, you may watch the two-part video solutions below.

Part 1: Q1 to Q5

Part 2: Q6 to Q10


Answers to the problems

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: $-1$.


Guided help on Trigonometry in Suresolv

To get the best results out of the extensive range of articles of tutorials, questions and solutions on Trigonometry in Suresolv, follow the guide,

Reading and Practice Guide on Trigonometry in Suresolv for SSC CHSL, SSC CGL, SSC CGL Tier II Other Competitive exams.

The guide list of articles is up-to-date.


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