## 1st preparatory SSC CGL level Questions with answers on Trigonometry 1

This is the 1st preparatory level question set with answers for SSC CGL exam and 1st on topic Trigonometry. You should refer to the tutorial, * Basic and rich concepts on Trigonometry* before going through this solution.

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 15 minutes.**When the time limit of 15 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 15 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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### 1st question set- 10 preparatory level problems for SSC CGL exam: 1st on Trigonometry - testing time 15 mins

#### Problem 1.

If $sin (A+B)=sin Acos B + cos Asin B$, then the value of $\sin 75^0$ is,

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

#### Problem 2.

If the $A$, $B$, $C$ and $D$ are the angles of a cyclic quadrilateral, the value of $cos A + cos B + cos C + cos D$ is,

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

#### Problem 3.

If $cos^2 \alpha - sin^2 \alpha = tan^2 \beta$, then the value of $cos^2 \beta - sin^2 \beta$ is,

- $cot^2 \beta$
- $tan^2 \alpha$
- $cot^2 \alpha$
- $tan^2 \beta$

#### Problem 4.

If $cos^4 \theta - sin^4 \theta=\displaystyle\frac{2}{3}$, then the value of $1 - 2sin^2 \theta$ is,

- $\displaystyle\frac{2}{3}$
- $\displaystyle\frac{3}{2}$
- $0$
- $1$

#### Problem 5.

If $x=asec \theta$ and $y=btan \theta$, then $\displaystyle\frac{x^2}{a^2}-\displaystyle\frac{y^2}{b^2}$ is,

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

#### Problem 6.

The value of $\displaystyle\frac{\sin \theta - 2sin^3 \theta}{2cos^3 \theta - cos \theta}$ is,

- $sin \theta$
- $cot \theta$
- $cos \theta$
- $tan \theta$

#### Problem 7.

If $sin \theta + cos \theta=p$ and $sec \theta + cosec \theta=q$, then the value of $q(p^2 - 1)$ is,

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

#### Problem 8.

If $sin (3\alpha - \beta)=1$, and $\cos (2\alpha + \beta)=\displaystyle\frac{1}{2}$, then the value of $tan \alpha$ is,

- $0$
- $\displaystyle\frac{1}{\sqrt{3}}$
- $\sqrt{3}$
- $1$

#### Problem 9.

If $rsin \theta =\displaystyle\frac{7}{2}$ and $rcos \theta =\displaystyle\frac{7\sqrt{3}}{2}$, then the value of $r$ is,

- $3$
- $4$
- $5$
- $7$

#### Problem 10.

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

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

**Key concepts and techniques used:** *Complementary trigonometric functions -- basic trigonometry concepts.*

**Note:** You will observe that in many of the Trigonometric problems basic and rich algebraic concepts and techniques are to be used. In fact that is the norm. Algebraic concepts are frequently used for quick solutions of Trigonometric problems.

For detailed conceptual solutions you may refer to the companion solution set, * Preparatory SSC CGL level Solution set 1 Trigonometry 1*.

### Answers to the questions

**Problem 1. Answer:** Option d: $\displaystyle\frac{\sqrt{3}+1}{2\sqrt{2}}$.

**Problem 2. Answer:** Option b: $0$.

**Problem 3. Answer:** Option b: $tan^2 \alpha$.

**Problem 4. Answer:** Option a: $\displaystyle\frac{2}{3}$.

**Problem 5. Answer:** Option c: $1$.

**Problem 6. Answer:** Option d: $tan \theta$.

**Problem 7. Answer:** Option a: $2p$.

**Problem 8. Answer:** Option b: $\displaystyle\frac{1}{\sqrt{3}}$.

**Problem 9. Answer:** Option d: $7$.

**Problem 10. Answer:** Option c: $60^0$.

### Resources on Trigonometry and related topics

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

### Preparatory SSC CGL level question and solution sets on Trigonometry

**Preparatory SSC CGL level Solution set 1 Trigonometry 1**

**Preparatory SSC CGL level Question set 1 Trigonometry 1**

### Tutorials on Trigonometry

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

### General guidelines for success in SSC CGL and similar exams

**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.

All Trigonometry related materials are avalable on * Suresolv Trigonometry*. A large part of these are on SSC CGL.

### 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**