## 12th SSC CGL Tier II level Question Set, topic Trigonometry 3

This is the 12th question set for the 10 practice problem exercise for SSC CGL exam and 3rd on topic Trigonometry. The answers to the questions and link to the detailed solutions are given at the end.

We repeat the method of taking the test. It is important to follow result bearing methods even in practice test environment.

### Method of taking the test for getting the best results from the test:

**Before start,**you may refer to our tutorialor any short but good material to refresh your concepts if you so require.**Basic and rich Trigonometric concepts and 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 given at the end 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**

**You may refer to:**

* 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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### 12th question set- 10 problems for SSC CGL Tier II exam: 3rd on Trigonometry - testing time 12 mins

#### Problem 1.

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

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

#### Problem 2.

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

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

#### Problem 3.

If $cos \theta + sec \theta = 2$, then the value of $cos^5 \theta + sec^5 \theta$ is,

- $-2$
- $2$
- $1$
- $-1$

#### Problem 4.

$sin(\alpha + \beta -\gamma)=cos(\beta + \gamma -\alpha)=\displaystyle\frac{1}{2}$ and $tan(\gamma + \alpha -\beta)=1$. If $\alpha$, $\beta$ and $\gamma$ are positive acute angles, value of $2\alpha + \beta$ is,

- $105^0$
- $110^0$
- $115^0$
- $120^0$

#### Problem 5.

If $sin \theta + sin^2 \theta=1$, then the value of $cos^{12} \theta + 3cos^{10} \theta + 3cos^{8} \theta + cos^6 \theta - 1$ is,

- $1$
- $0$
- $2$
- $3$

#### Problem 6.

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,

- 4
- 0
- 2
- 1

#### Problem 7.

If $4cos^2 \theta - 4\sqrt{3}cos \theta + 3=0$ and $0^0 \leq \theta \leq 90^0$, then the value of $\theta$ is,

- $60^0$
- $90^0$
- $30^0$
- $45^0$

#### Problem 8.

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

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

#### Problem 9.

If $x=asin \theta-bcos \theta$ and $y=acos \theta + bsin \theta$, then which of the following is true?

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

#### Problem 10.

If $tan \theta=\displaystyle\frac{a}{b}$, then the value of $\displaystyle\frac{asin^3 \theta - bcos^3 \theta}{asin^3 \theta + bcos^3 \theta}$ is,

- $\displaystyle\frac{a^4-b^4}{a^4+b^4}$
- $\displaystyle\frac{a^3+b^3}{a^3-b^3}$
- $\displaystyle\frac{a^3-b^3}{a^3+b^3}$
- $\displaystyle\frac{a^4+b^4}{a^4-b^4}$

For detailed solutions refer to the companion **SSC CGL Tier II Solution set 12 Trigonometry 3, questions with solutions.**

You may also watch the video solutions at the two-part video below.

**Part 1: Q1 to Q5**

**Part 2: Q6 to Q10**

The answers to the questions are given below.

### Answers to the questions.

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

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

**Problem 3. Answer:** Option b: $2$.

**Problem 4. Answer:** Option d: $120^0$.

**Problem 5. Answer:** Option b: $0$.

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

**Problem 7. Answer:** Option c: $30^0$.

**Problem 8. Answer:** Option b: $\sqrt{2}+1$.

**Problem 9. Answer:** Option a: $x^2 + y^2=a^2 + b^2$.

**Problem 10. Answer:** Option a: $\displaystyle\frac{a^4-b^4}{a^4+b^4}$.

### 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 a difficult SSC CGL level problem in a few reasoned steps, Trigonometry 10**

**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 18 Trigonometry 4, questions with solutions**

**SSC CGL Tier II level Question Set 18 Trigonometry 4, questions with answers**

**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**

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#### 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**