## Sixteenth SSC CGL level Question Set on Trigonometry

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

We found from our analysis of the Trigonometry problems that this topic is built on a * small set of basic and rich concepts.* That's why it's possible to solve any problem in this topic area fast and quick, following elegant problem solving methods if you are used to applying problem solving techniques based on related basic and rich subject concepts.

We have tried to show you how this can be done in the solution set. But please, first take this test in prescribed time.

**Recommendation:** Before taking the test you should refer to the tutorial on,

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

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

### Sixteenth Question set- 10 problems for SSC CGL exam: topic Trigonometry - time 12 mins

**Problem 1.**

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

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

**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,

- $\displaystyle\frac{41}{40}$
- $\displaystyle\frac{40}{41}$
- $\displaystyle\frac{25}{16}$
- $\displaystyle\frac{41}{9}$

**Problem 3.**

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

- 100
- 3
- 2
- 1

**Problem 4.**

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

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

**Problem 5.**

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

- $x - y$
- $\displaystyle\frac{x - y}{\sqrt{x^2 + y^2}}$
- $\displaystyle\frac{y - x}{\sqrt{x^2 + y^2}}$
- $x + y$

**Problem 6.**

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

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

**Problem 7.**

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

- $\displaystyle\frac{y^2}{x\sqrt{y^2 - x^2}}$
- $\displaystyle\frac{x^2}{y\sqrt{y^2 - x^2}}$
- $\displaystyle\frac{x^2}{y\sqrt{x^2 - y^2}}$
- $\displaystyle\frac{y^2}{x\sqrt{x^2 - y^2}}$

**Problem 8.**

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

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

**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,

- $1$
- $tan A.tan B.tan C$
- $cos A.cos B.cos C$
- $sin A.sin B.sin C$

**Problem 10.**

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

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

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.

Watch the **video solutions** in the **two-part video.**

**Part 1: Q1 to Q5**

**Part 2: Q6 to Q10**

### Answers to the questions

**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,*

**The guide list of articles is up-to-date.**