SSC CGL level Question Set 65, Trigonometry 6 | SureSolv

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SSC CGL level Question Set 65, Trigonometry 6

65th SSC CGL level Question Set, topic Trigonometry 6

ssc cgl level question set 65 trigonometry 6

This is the 65th question set for the 10 practice problem exercise for SSC CGL exam and 6th on topic Trigonometry. You will find the answers to the questions along with list of related readings including the detailed conceptual solutions after the questions.

Before taking the test it is recommended that you refer to the tutorials,

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

Tutorial on Basic and rich concepts in Trigonometry part 2, proof of compound angle functions

Tutorial on 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. It is not difficult.


65th question set- 10 problems for SSC CGL exam: 6th on Trigonometry - testing time 12 mins

Problem 1.

If $2-cos^2 \theta=3sin \theta{cos \theta}$, where $sin \theta \neq cos \theta$, the value of $tan \theta$ is,

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

Problem 2.

If $sin \theta + cos \theta =\sqrt{2}cos(90^0- \theta)$, then $cot \theta$ is,

  1. $\sqrt{2}-1$
  2. $\sqrt{2}+1$
  3. $0$
  4. $\sqrt{2}$

Problem 3.

If $(a^2-b^2)sin \theta + 2abcos \theta=a^2+b^2$ then the value of $tan \theta$ is,

  1. $\displaystyle\frac{1}{2ab}(a^2+b^2)$
  2. $\displaystyle\frac{1}{2}(a^2-b^2)$
  3. $\displaystyle\frac{1}{2}(a^2+b^2)$
  4. $\displaystyle\frac{1}{2ab}(a^2-b^2)$

Problem 4.

The value of $sec \theta\left(\displaystyle\frac{1+sin \theta}{cos \theta}+\displaystyle\frac{cos \theta}{1+sin \theta}\right) - 2tan^2 \theta$ is,

  1. 4
  2. 0
  3. 2
  4. 1

Problem 5.

If $cot \theta + cosec \theta =3$, and $\theta$ an acute angle, the value of $cos \theta$ is,

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

Problem 6.

If $xcos \theta - sin \theta=1$, then the value of $x^2-(1+x^2)sin \theta$ is,

  1. $1$
  2. $0$
  3. $2$
  4. $-1$

Problem 7.

If $\theta=60^0$, then the value of $\displaystyle\frac{1}{2}\sqrt{1+ sin \theta} + \displaystyle\frac{1}{2}\sqrt{1- sin \theta}$ is,

  1. $cot \displaystyle\frac{\theta}{2}$
  2. $cos \displaystyle\frac{\theta}{2}$
  3. $sec \displaystyle\frac{\theta}{2}$
  4. $sin \displaystyle\frac{\theta}{2}$

Problem 8.

If $3sin \theta + 5cos \theta =5$, ($0\lt \theta \lt 90^0$), then the value of $5sin \theta-3cos \theta$ will be,

  1. 1
  2. 2
  3. 5
  4. 3

Problem 9.

If $tan \theta = \displaystyle\frac{1}{\sqrt{11}}$, and $0\lt \theta \lt 90^0$, then the value of $\displaystyle\frac{cosec^2 \theta - sec^2 \theta}{cosec^2 \theta + sec^2 \theta}$ is,

  1. $\displaystyle\frac{5}{6}$
  2. $\displaystyle\frac{3}{4}$
  3. $\displaystyle\frac{4}{5}$
  4. $\displaystyle\frac{6}{7}$

Problem 10.

If $tan^2 \theta=1-e^2$, then the value of $sec \theta + tan^3 \theta{cosec \theta}$ is equal to,

  1. $(2+e^2)^{\frac{3}{2}}$
  2. $(2+e^2)^{\frac{1}{2}}$
  3. $(2-e^2)^{\frac{3}{2}}$
  4. $(2-e^2)^{\frac{1}{2}}$

The answers to the questions are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL level Solution Set 65 on Trigonometry 6.

If you like, you may also watch the video solutions in the two-part video below.

Part1: Q1 to Q5

Part 2: Q6 to Q10


Answers to the questions

Problem 1. Answer: b: $\displaystyle\frac{1}{2}$.

Problem 2. Answer: a: $\sqrt{2}-1$.

Problem 3. Answer: d: $\displaystyle\frac{1}{2ab}(a^2-b^2)$.

Problem 4. Answer: Option c: 2.

Problem 5. Answer: c: $\displaystyle\frac{4}{5}$.

Problem 6. Answer: a: $1$.

Problem 7. Answer: b: $cos \displaystyle\frac{\theta}{2}$.

Problem 8. Answer: d: 3.

Problem 9. Answer: a: $\displaystyle\frac{5}{6}$.

Problem 10. Answer: c: $(2-e^2)^{\frac{3}{2}}$.


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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