SSC CGL level Question Set 40, Trigonometry 4 | SureSolv

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SSC CGL level Question Set 40, Trigonometry 4

40th SSC CGL level Question Set, topic Trigonometry 4

SSC-CGL-question-set-40-trigonometry4.jpg

This is the 40th question set for the 10 practice problem exercise for SSC CGL exam and 4th on topic Trigonometry.

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.


40th question set- 10 problems for SSC CGL exam: 4th on Trigonometry - test time 12 mins

Problem 1.

If $cosec 39^0=p$, the value of, $\displaystyle\frac{1}{cosec^2 51^0} + sin^2 39^0 + tan^2 51^0 - \displaystyle\frac{1}{sin^2 51^0 sec^2 39^0}$ is,

  1. $p^2 - 1$
  2. $\sqrt{p^2 - 1}$
  3. $1-p^2$
  4. $\sqrt{1-p^2}$

Problem 2.

If $sec \theta=x + \displaystyle\frac{1}{4x}$, where $(0^0 \lt \theta \lt 90^0)$, then $sec \theta + tan \theta$ is,

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

Problem 3.

If $tan \theta=1$, then the value of $\displaystyle\frac{8sin \theta + 5cos \theta}{sin^3 \theta -2cos^3 \theta + 7cos \theta}$ is,

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

Problem 4.

If $7sin \theta = 24cos \theta$, where $0 \lt \theta \lt \displaystyle\frac{\pi}{2}$, then the value of $14tan \theta - 75cos \theta - 7sec \theta$ is,

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

Problem 5.

The minimum value of $sin^2 \theta + cos^2 \theta + sec^2 \theta + cosec^2 \theta + tan^2 \theta + cot^2 \theta$ is equal to,

  1. 1
  2. 7
  3. 3
  4. 5

Problem 6.

In a right $\triangle ABC$ with right angle at $\angle ABC$, if $AB=2\sqrt{6}$ and $AC - BC = 2$ then, $sec A + tan A$ is,

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

Problem 7.

If $tan 2\theta . tan 4\theta = 1$, then the value of $tan 3\theta$ is,

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

Problem 8.

If $sin \displaystyle\frac{\pi x}{2}=x^2 -2x +2$, then the value of $x$ is,

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

Problem 9.

If $2sin \theta + cos \theta = \displaystyle\frac{7}{3}$, then the value of $(tan^2 \theta - sec^2 \theta)$ is,

  1. $0$
  2. $\displaystyle\frac{7}{3}$
  3. $\displaystyle\frac{3}{7}$
  4. $-1$

Problem 10.

If $(rcos \theta - \sqrt{3})^2 + (rsin \theta - 1)^2 = 0$, then the value of $\displaystyle\frac{rtan \theta + sec \theta}{rsec \theta + tan \theta}$ is,

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

The answers are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL level Solution Set 40 on Trigonometry 4.

You may also watch video solutions in the two-part video.

Part 1: Q1 to Q5

Part 2: Q6 to Q10


Answers to the questions

Problem 1. Ans: Option a: $p^2 - 1$.

Problem 2. Ans: Option b: $2x$.

Problem 3. Ans: Option b: 2.

Problem 4. Ans: Option c: 2.

Problem 5. Ans: Option b: 7.

Problem 6. Ans: Option c: $\sqrt{6}$.

Problem 7. Ans: Option d: 1.

Problem 8. Ans: Option c: 1.

Problem 9. Ans: Option d: $-1$.

Problem 10. Ans: Option a: $\displaystyle\frac{4}{5}$.


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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