Trigonometry questions for SSC CGL with answers Set 2 | SureSolv

You are here

SSC CGL level Question Set 16, Trigonometry

Trigonometry questions for SSC CGL with answers set 2

Trigonometry questions for SSC CGL with answers Set 2

Solve 10 trigonometry questions for SSC CGL Set 2 in 12 minutes. Verify your answers. Learn how to solve the question in time from paired solution set.

For best results, take the timed test first, score your performance with 1 for each correct answer, negative 0.25 for each wrong answer and finally clear up your doubts and learn how to solve the questions quickly from the paired solution set.

The answers and link to the solutions are at the end.

10 Trigonometry questions for SSC CGL Set 2 - time to solve 12 mins

Problem 1.

The simplified value of $(sec\theta - cos\theta)^2 + (cosec\theta - sin\theta)^2 - (cot\theta - tan\theta)^2$ is,

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

Problem 2.

If $\displaystyle\frac{sin\theta + cos\theta}{sin\theta - cos\theta} = \frac{5}{4}$, then the value of $\displaystyle\frac{tan^2\theta + 1}{tan^2\theta - 1}$ will be,

  1. $\displaystyle\frac{41}{40}$
  2. $\displaystyle\frac{40}{41}$
  3. $\displaystyle\frac{25}{16}$
  4. $\displaystyle\frac{41}{9}$

Problem 3.

If $sin\theta + cosec\theta =2$, then the value of $sin^{100}\theta + cosec^{100}\theta$ is,

  1. 100
  2. 3
  3. 2
  4. 1

Problem 4.

The greatest value of $sin^4\theta + cos^4\theta$ is,

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

Problem 5.

If $\displaystyle\frac{sin\theta}{x} = \displaystyle\frac{cos\theta}{y}$, then $sin\theta - cos\theta$ is,

  1. $x - y$
  2. $\displaystyle\frac{x - y}{\sqrt{x^2 + y^2}}$
  3. $\displaystyle\frac{y - x}{\sqrt{x^2 + y^2}}$
  4. $x + y$

Problem 6.

If $tan\theta - cot\theta = 0$ find the value of $sin\theta + cos\theta$.

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

Problem 7.

If $sin21^0 = \displaystyle\frac{x}{y}$ then $sec21^0 - sin69^0$ is,

  1. $\displaystyle\frac{y^2}{x\sqrt{y^2 - x^2}}$
  2. $\displaystyle\frac{x^2}{y\sqrt{y^2 - x^2}}$
  3. $\displaystyle\frac{x^2}{y\sqrt{x^2 - y^2}}$
  4. $\displaystyle\frac{y^2}{x\sqrt{x^2 - y^2}}$

Problem 8.

If $\displaystyle\frac{sec\theta+ tan\theta}{sec\theta - tan\theta}=\displaystyle\frac{5}{3}$ then $sin\theta$ is,

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

Problem 9.

If $(1 + sin A)(1 + sin B)(1 + sin C) = (1 - sin A)(1 - sin B)( 1 - sin C)$, then the expression on each side of the equation equals,

  1. $1$
  2. $tan A.tan B.tan C$
  3. $cos A.cos B.cos C$
  4. $sin A.sin B.sin C$

Problem 10.

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

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

You will find the detailed conceptual solutions to these questions in SSC CGL level Solution Set 16 on Trigonometry.

Note: You will observe that in many of the Trigonometric problems rich algebraic concepts and techniques are to be used. In fact that is the norm. Algebraic concepts are frequently used for elegant solutions of Trigonometric problems. But compared to difficulties of purely algebraic problem solving, trigonometry problems are simpler because by applying a few basic and rich trigonometric concepts along with algebraic concepts elegant solutions are reached faster.


Answers to the 10 Trigonometry questions for SSC CGL Set 2

Problem 1. Answer: Option d: $1$.

Problem 2. Answer: Option a : $\displaystyle\frac{41}{40}$.

Problem 3. Answer: Option c: 2.

Problem 4. Answer: Option a: $1$.

Problem 5. Answer: Option b: $\displaystyle\frac{x - y}{\sqrt{x^2 + y^2}}$.

Problem 6. Answer: Option a : $\sqrt{2}$.

Problem 7. Answer: Option b: $\displaystyle\frac{x^2}{y\sqrt{y^2 - x^2}}$.

Problem 8. Answer: Option d: $\displaystyle\frac{1}{4}$.

Problem 9. Answer: Option c: $cos A.cos B.cos C$.

Problem 10. Answer: Option a: $cos\displaystyle\frac{\theta}{2}$.


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.