## 82nd SSC CGL level Question Set, Trigonometry 8

This is the 82nd question set for the 10 practice problem exercise for SSC CGL exam and 8th on topic Trigonometry. You should take the test first and then only go through its paired solution set to gain maximum benefits from this resource. The answers to the questions and link to the solutions are given at the end.

Answer carefully. Some of the questions may seem to be difficult, but with a bit of ingenuity can be solved quickly.

**Recommended:** Before taking the test you may refer to our comprehensive tutorial on Trigonometric concepts and methods,

**Basic and rich Trigonometry concepts and applications.**

### 82nd question setâ€”10 problems for SSC CGL exam: 8th on Trigonometryâ€”testing time 15 mins

**Problem 1.**

If $(1+\tan^2 \theta)=\displaystyle\frac{625}{49}$, then the value of $(\sqrt{\sin \theta +\cos \theta})$, where $\theta$ is acute, is,

- $\displaystyle\frac{5}{7}$
- $\displaystyle\frac{\sqrt{31}}{5}$
- $1$
- $\displaystyle\frac{5}{4}\sqrt{\displaystyle\frac{31}{42}}$

**Problem 2.**

If $2\text{cosec }^2 \theta=x$, then the value of $x$ is,

- $\displaystyle\frac{\sec \theta}{\sec \theta -1}+\displaystyle\frac{\sec \theta}{\sec \theta+1}$
- $\displaystyle\frac{\text{cosec } \theta}{\text{cosec } \theta-1}+\displaystyle\frac{\text{cosec } \theta}{\text{cosec } \theta+1}$
- $\displaystyle\frac{\text{cosec } \theta}{\sec \theta-1}+\displaystyle\frac{\text{cosec } \theta}{\sec \theta+1}$
- $\displaystyle\frac{\sec \theta}{\text{cosec } \theta-1}+\displaystyle\frac{\sec \theta}{\text{cosec } \theta+1}$

**Problem 3.**

If $\cos \left(\displaystyle\frac{\theta}{2}\right)=x$ then the value of $x$ is,

- $\sqrt{\displaystyle\frac{1+\cos \theta}{2}}$
- $\sqrt{\displaystyle\frac{1-\sin \theta}{2}}$
- $\sqrt{\displaystyle\frac{1-\cos \theta}{2}}$
- $\sqrt{\displaystyle\frac{1+\sin \theta}{2}}$

**Problem 4.**

If $x$ and $y$ are positive acute angles such that $\sin (2x+3y)=\displaystyle\frac{\sqrt{3}}{2}$ and $\cos (4x-3y)=\displaystyle\frac{\sqrt{3}}{2}$, then the value of $\tan (6x-3y)$ is,

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

**Problem 5.**

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

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

**Problem 6.**

If $\text{cot } \alpha=\left(\displaystyle\frac{\sin \beta}{1-\cos \beta}\right)$, then the value of $\text{cot } 2\alpha$ is,

- $\text{cot } \beta$
- $\tan \beta$
- $\text{cot } 2\beta$
- $\text{cot } \displaystyle\frac{\beta}{2}$

**Problem 7.**

The simplified value of $\left(\displaystyle\frac{1}{\sec \theta+\tan \theta}\right)^2$ is,

- $\sec \theta+\tan \theta$
- $\sin \theta\cos \theta$
- $\displaystyle\frac{1-\cos \theta}{1+\cos \theta}$
- $\displaystyle\frac{1-\sin \theta}{1+\sin \theta}$

**Problem 8.**

The simplified value of $(\sec \theta-cos \theta)(\sec \theta+\cos \theta)$ is,

- $2\tan^2 \theta$
- $\sin^2 \theta+\tan^2 \theta$
- $\sin^2 \theta\tan^2 \theta$
- $2\sin^2 \theta$

**Problem 9.**

The simplified value of $\displaystyle\frac{\tan \theta}{1-\text{cot }\theta}+\displaystyle\frac{\text{cot } \theta}{1-\tan\theta}-\displaystyle\frac{2}{\sin \theta}$ is,

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

**Problem 10.**

If $\text{cosec }\theta+\text{cosec}^2 \theta=1$, then the value of, $(\text{cot}^{12} \theta-3\text{cot}^{10} \theta+3\text{cot}^{8} \theta-\text{cot}^{6} \theta)$ is,

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

The answers to the questions are given below. To know how to solve these questions quickly, refer to the corresponding solution set,

**SSC CGL level Solution set 82 Trigonometry 8.**

### Answers to the questions

**Problem 1. Answer:** Option b: $\displaystyle\frac{\sqrt{31}}{5}$.

**Problem 2. Answer:** Option a: $\displaystyle\frac{\sec \theta}{\sec \theta -1}+\displaystyle\frac{\sec \theta}{\sec \theta+1}$.

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

**Problem 4. Answer:** Option c: $\sqrt{3}$.

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

**Problem 6. Answer:** Option a: $\text{cot }\beta$.

**Problem 7. Answer:** Option d: $\displaystyle\frac{1-\sin \theta}{1+\sin \theta}$.

**Problem 8. Answer:** Option b: $\sin^2 \theta+\tan^2 \theta$.

**Problem 9. Answer:** Option d: $1$.

**Problem 10. Answer:** Option a: $1$.

### Resources on Trigonometry and related topics

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

#### Tutorials on Trigonometry

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