## 56th SSC CGL level Question Set, topic Trigonometry 5

This is the 56th question set for the 10 practice problem exercise for SSC CGL exam and 5th on topic Trigonometry.

We repeat the method of taking the test. It is an important * Test preparation method* to follow

**even in practice test**environment

*as metrics or performance measurement is built-in.*

**for continuous skill-set improvement,**### Method of taking the test for getting the best results from the test:

**Before start,**go throughor any short but good material to refresh your concepts if you so require.**Tutorial on Basic and rich concepts in Trigonometry and its applications****Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 12 minutes.**When the time limit of 12 minutes is over,**mark up to which you have answered,**but go on to complete the set.****At the end,**refer to the answers from the companion solution set to mark your score at 12 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you can get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

**Resources that should be useful for you**

#### 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, proof of compound angle functions**

**Tutorial on Trigonometry concepts part 3, maxima or minima of Trigonometric expressions**

**You may also refer to the related resources:**

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

*to access all the valuable student resources that we have created specifically for SSC CGL, but*

**section on SSC CGL****generally for any hard MCQ test.**

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Now set the stopwatch alarm and start taking this test. It is not difficult.

### 56th question set- 10 problems for SSC CGL exam: 5th on Trigonometry - testing time 12 mins

**Problem 1.**

The maximum value of $(2\sin \theta + 3\cos\theta)$ is,

- $1$
- $2$
- $\sqrt{13}$
- $\sqrt{15}$

**Problem 2.**

Find the minimum value of $9\tan^2 \theta + 4\cot^2 \theta$,

- $15$
- $6$
- $9$
- $12$

**Problem 3.**

If $\text{cosec} \theta -\cot \theta= \displaystyle\frac{7}{2}$, the value of $\text{cosec} \theta$ is,

- $\displaystyle\frac{49}{28}$
- $\displaystyle\frac{53}{28}$
- $\displaystyle\frac{47}{28}$
- $\displaystyle\frac{51}{28}$

**Problem 4.**

If $\tan^2 \alpha=1 +2\tan^2 \beta$, where $\alpha$ and $\beta$ both are positive acute angles, find the value of $\sqrt{2}\cos \alpha - \cos \beta$.

- $0$
- $\sqrt{2}$
- $-1$
- $1$

**Problem 5.**

The value of $152(\sin 30^0 + 2\cos^2 45^0 + 3\sin 30^0 +$

$\hspace{30mm}4\cos^2 45^0 + ....+17\sin 30^0+18\cos^2 45^0)$ is,

- an irrational number
- a rational number but not an integer
- an integer but not a perfect square
- the perfect square of an integer

**Problem 6.**

If $\tan \theta + \cot \theta=2$, then the value of $\tan^n \theta + \cot^n \theta$ ($0^0 \lt \theta \lt 90^0$, and $n$ an integer) is,

- $2$
- $2^{n+1}$
- $2^n$
- $2n$

**Problem 7.**

If $\displaystyle\frac{\sin \theta}{1+\cos \theta} + \displaystyle\frac{\sin \theta}{1-\cos \theta} = 4$, the value of $\cot \theta + \sec \theta$ is,

- $\sqrt{3}$
- $\displaystyle\frac{\sqrt{3}}{7}$
- $\displaystyle\frac{\sqrt{3}}{5}$
- $\displaystyle\frac{5}{\sqrt{3}}$

**Problem 8.**

If $\sin \theta + \cos \theta =\sqrt{2}$ with $\angle \theta$ a positive acute angle, then the value of $\tan \theta + \sec \theta$ is,

- $\sqrt{3}-1$
- $\displaystyle\frac{1}{\sqrt{2}-1}$
- $\sqrt{2}-1$
- $\sqrt{3}+1$

**Problem 9.**

If $p=a\sec {\theta}\cos \alpha$, $q =b\sec {\theta}\sin \alpha$, and $r =c\tan \theta$, then the value of $\displaystyle\frac{p^2}{a^2} +\displaystyle\frac{q^2}{b^2}-\displaystyle\frac{r^2}{c^2}$ is,

- 0
- 1
- 4
- 5

**Problem 10.**

$\displaystyle\frac{\sin^2 \theta}{\cos^2 \theta}+\displaystyle\frac{\cos^2 \theta}{\sin^2 \theta}$ is equal to,

- $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta}$
- $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta} -2$
- $\displaystyle\frac{1}{\tan^2 \theta - \cot^2 \theta}$
- $\displaystyle\frac{\sin^2 \theta}{\cot \theta - \sec \theta}$

You will find answers and the detailed conceptual solutions to these questions in * SSC CGL level Solution Set 56 on Trigonometry 5*.

### Answers to the questions

**Problem 1. Answer:** c: $\sqrt{13}$.

**Problem 2. Answer:** d: $12$.

**Problem 3. Answer:** b: $\displaystyle\frac{53}{28}$.

**Problem 4. Answer:** a: $0$.

**Problem 5. Answer:** d: the perfect square of an integer.

**Problem 6. Answer:** a: $2$.

**Problem 7. Answer:** d: $\displaystyle\frac{5}{\sqrt{3}}$.

**Problem 8. Answer:** b: $\displaystyle\frac{1}{\sqrt{2}-1}$.

**Problem 9. Answer:** b: 1.

**Problem 10. Answer:** b: $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta}-2$.

### 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**

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