## Second SSC CGL level Question Set, topic Trigonometry

This is the second Question set of 10 practice problem exercise for SSC CGL exam on topic Trigonometry. Students must complete the this set in prescribed time first and then only refer to the corresponding solution set.

It is emphasized here that answering in MCQ test is not at all the same as answering in a school test where you need to derive the solution in perfectly elaborated steps.

In MCQ test instead, you need basically to deduce the answer in shortest possible time and select the right choice. None will ask you about what steps you followed.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts of the topics
- is adequately fast in mental math calculation
- should try to solve each problem using the most basic concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his head rather than on paper.

Actual problem solving happens in items 3 and 4 above. But how to do that?

You need to use your **your problem solving abilities** only. There is no other recourse.

**Recommendation:** Before taking the test you may refer to the tutorial on * Basic and rich concepts in Trigonometry and its applications*.

### Second Question set- 10 problems for SSC CGL exam: topic Trigonometry - time 20 mins

**Q1.** If $0^0 < \theta < 90^0$ and $2sin^2\theta + 3cos\theta = 3$ then the value of $\theta$ is,

- $30^0$
- $60^0$
- $45^0$
- $75^0$

**Q2.** If $sin\theta=\displaystyle\frac{a}{\sqrt{a^2 + b^2}}$, then the value of $cot\theta$ will be,

- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{a}{b}$
- $\displaystyle\frac{a}{b} + 1$
- $\displaystyle\frac{b}{a} + 1$

**Q3.** If $tan\theta=\frac{3}{4}$ and $0<\theta<\frac{\pi}{2}$ and $25xsin^2\theta{cos\theta}=tan^2\theta$, then the value of $x$ is,

- $\frac{7}{64}$
- $\frac{9}{64}$
- $\frac{3}{64}$
- $\frac{5}{64}$

**Q4.** If $xsin\theta - ycos\theta = \displaystyle\sqrt{x^2 + y^2}$ and $\displaystyle\frac{cos^2\theta}{a^2} + \frac{sin^2\theta}{b^2} = \frac{1}{x^2 + y^2}$ then,

- $\displaystyle\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$
- $\displaystyle\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} - \frac{y^2}{a^2} = 1$

**Q5.** The value of $sin^21^0+sin^23^0+sin^25^0+...$

$...+sin^287^0+sin^289^0$ is,

- $22$
- $22\frac{1}{2}$
- $23$
- $22\frac{1}{4}$

**Q6.** The minimum value of $cos^2\theta + sec^2\theta$ is,

- 0
- 1
- 2
- 3

**Q7.** If $cos\theta + sec\theta = 2$ $(0^0\leq{\theta}\leq{90^0})$ then the value of $cos{10}\theta + sec{11}\theta$ is,

- 0
- 1
- 2
- -1

**Q8.** If $tan\theta=\frac{3}{4}$ and $\theta$ is acute then, $cosec\theta$ is equal to,

- $\frac{5}{3}$
- $\frac{5}{4}$
- $\frac{4}{3}$
- $\frac{4}{5}$

**Q9.** If $\displaystyle\frac{sin\theta + cos\theta}{sin\theta - cos\theta} = 3$ then the numerical value of $sin^4\theta - cos^4\theta$ is,

- $\frac{1}{2}$
- $\frac{2}{5}$
- $\frac{3}{5}$
- $\frac{4}{5}$

**Q10.** The minimum value of $2sin^2\theta + 3cos^2\theta$ is,

- 0
- 3
- 2
- 1

You will find the detailed conceptual solutions to these questions inĀ * SSC CGL level Solution Set 2 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.

### Answers to the questions

**Problem 1. Answer:** Option b: $60^0$.

**Problem 2. Answer:** Option a : $\frac{b}{a}$.

**Problem 3. Answer:** Option d: $\frac{5}{64}$.

**Problem 4. Answer:** Option b: $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$.

**Problem 5. Answer:** Option b: $22\frac{1}{2}$.

**Problem 6. Answer:** Option c : 2.

**Problem 7. Answer:** Option c: 2.

**Problem 8. Answer:** Option a: $\frac{5}{3}$.

**Problem 9. Answer:** Option c: $\frac{3}{5}$.

**Problem 10. Answer:** Option c: 2.

### Resources on Trigonometry and related topics

You may refer to our useful resources on Trigonometry and other related topics especially algebra.

#### Tutorials on Trigonometry

**Basic and rich concepts in Trigonometry and its applications**

**Basic and Rich Concepts in Trigonometry part 2, proof of compound angle functions**

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

#### General guidelines for success in SSC CGL

**7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests**

#### Efficient problem solving in Trigonometry

**How to solve not so difficult SSC CGL level problem in a few light steps, Trigonometry 9**

**How to solve a difficult SSC CGL level problem in a few conceptual steps, Trigonometry 8 **

**How to solve not so difficult SSC CGL level problem in a few light steps, Trigonometry 7**

**How to solve a difficult SSC CGL level problem in few quick steps, Trigonometry 6**

**How to solve a School Math problem in a few direct steps, Trigonometry 5**

**How to solve difficult SSC CGL level School math problems in a few quick steps, Trigonometry 5**

**How to solve School Math problem in a few steps and in Many Ways, Trigonometry 4**

**How to solve a School Math problem in a few simple steps, Trigonometry 3**

**How to solve difficult SSC CGL level School math problems in a few simple steps, Trigonometry 4**

**How to solve difficult SSC CGL level School math problems in a few simple steps, Trigonometry 3**

**How to solve School math problems in a few simple steps, Trigonometry 2**

**How to solve School math problems in a few simple steps, Trigonometry 1**

**A note on usability:** The *Efficient math problem solving* sessions on **School maths** are **equally usable for SSC CGL aspirants**, as firstly, the "Prove the identity" problems can easily be converted to a MCQ type question, and secondly, the same set of problem solving reasoning and techniques have been used for any efficient Trigonometry problem solving.

#### SSC CGL Tier II level question and solution sets on Trigonometry

**SSC CGL Tier II level Solution set 12 Trigonometry 3, questions with solutions**

**SSC CGL Tier II level Question set 12 Trigonometry 3, questions with answers**

**SSC CGL Tier II level Solution set 11 Trigonometry 2**

**SSC CGL Tier II level Question set 11 Trigonometry 2**

**SSC CGL Tier II level Solution set 7 Trigonometry 1**

**SSC CGL Tier II level Question set 7 Trigonometry 1**

#### SSC CGL level question and solution sets in Trigonometry

**SSC CGL level solution set 77 on Trigonometry 7**

**SSC CGL level question set 77 on Trigonometry 7**

**SSC CGL level Solution Set 65 on Trigonometry 6**

**SSC CGL level Question Set 65 on Trigonometry 6**

**SSC CGL level Solution Set 56 on Trigonometry 5**

**SSC CGL level Question Set 56 on Trigonometry 5**

**SSC CGL level Solution Set 40 on Trigonometry 4**

**SSC CGL level Question Set 40 on Trigonometry 4**

**SSC CGL level Solution Set 19 on Trigonometry**

**SSC CGL level Question set 19 on Trigonometry**

**SSC CGL level Solution Set 16 on Trigonometry**

**SSC CGL level Question Set 16 on Trigonometry**

**SSC CGL level Question Set 2 on Trigonometry**

**SSC CGL level Solution Set 2 on Trigonometry**

#### Algebraic concepts

**Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems**

**More rich algebraic concepts and techniques for elega****n****t solutions of SSC CGL problems**