## 18th SSC CGL Tier II level Question Set, topic Trigonometry 4, questions with answers

This is the 18th question set for the 10 practice problem exercise for SSC CGL Tier II exam and 4th on topic Trigonometry. Some of these 10 questions may seem to be a bit more difficult.

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

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

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

The test should be used as a mini-mock test and answering timed with the timer on. When the time is over, don't stop answering. Just mark the point up to which you have answered in the scheduled time and go on to complete the test.

After the test, score yourself on your answer in scheduled time and analyze all the difficulties by going through the corresponding solution set (link given at the end).

Now set the timer on and start taking the test.

### 18th question set- 10 problems for SSC CGL Tier II exam: 4th on Trigonometry - testing time 12 mins

#### Problem 1.

The value of

$\displaystyle\frac{4\cos(90^0- \theta)\sin^3(90^0+\theta)-4\sin(90^0+\theta)\cos^3(90^0-\theta)}{\cos\left(\displaystyle\frac{180^0+8\theta}{2}\right)}$ is,

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

#### Problem 2.

If $\sec \theta(\cos \theta+\sin \theta)=\sqrt{2}$ then the value of $\displaystyle\frac{2\sin \theta}{\cos \theta -\sin \theta}$ is equal to,

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

**Problem 3.**

The value of $\displaystyle\frac{(\sin x+\sin y)(\sin x - \sin y)}{(\cos x+\cos y)(\cos y - \cos x)}$ is,

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

#### Problem 4.

The value of $\displaystyle\frac{1}{\sin^4(90^0-\theta)}+\displaystyle\frac{1}{\cos^2(90^0-\theta)-1}$ is,

- $\tan^4 \theta$
- $\tan^2 \theta\sec^2 \theta$
- $\sec^4 \theta$
- $\tan^2 \theta\sin^2 \theta$

#### Problem 5.

The value of $\sin(B-C)\cos(A-D)$

$\hspace{22mm}+\sin(A-B)\cos(C-D)$

$\hspace{22mm}+\sin(C-A)\cos(B-D)$ is,

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

#### Problem 6.

The value of $\left[\tan^2(90^0-\theta)-\sin^2(90^0-\theta)\right]$

$\hspace{22mm}\times{\text{cosec}^2(90^0-\theta)\text{cot}^2(90^0-\theta)}$ is,

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

#### Problem 7.

The value of $\displaystyle\frac{4}{3}\text{cot}^2\left(\displaystyle\frac{\pi}{6}\right)+3\cos^2(150^0)$

$\hspace{22mm}-4\text{cosec}^245^0+8\sin\left(\displaystyle\frac{\pi}{2}\right)$ is,

- $1$
- $\displaystyle\frac{13}{2}$
- $-\displaystyle\frac{7}{2}$
- $\displaystyle\frac{25}{4}$

#### Problem 8.

The value of $\displaystyle\frac{\tan 5\theta+\tan 3\theta}{4\cos 4\theta(\tan 5\theta-\tan 3\theta)}$ is,

- $\tan 4\theta$
- $\sin 2\theta$
- $\cos 2\theta$
- $\text{cot }2\theta$

#### Problem 9.

The value of $\displaystyle\frac{\sin(y-z)+\sin(y+z)+2\sin y}{\sin(x-z)+\sin(x-z)+2\sin x}$ is,

- $\cos x\sin y$
- $\sin x\tan y$
- $\sin z$
- $\displaystyle\frac{\sin y}{\sin x}$

#### Problem 10.

The value of $\displaystyle\frac{\sin(90^0-10\theta)-\cos(\pi-6\theta)}{\cos\left(\displaystyle\frac{\pi}{2}-10\theta\right)-\sin(\pi-6\theta)}$ is,

- $\cos \theta$
- $\tan 2\theta$
- $\text{cot }3\theta$
- $\text{cot }2\theta$

The conceptual solutions to the questions are available at * SSC CGL Tier II Solution Set 18 Trigonometry 4*, and the answers are given below.

You may watch the video solutions in the two-part video below.

**Part 1: Q1 to Q5**

**Pat 2: Q6 to Q10**

### Answers to the questions

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

**Problem 2.** **Answer:** Option a: $\sqrt{2}$.

**Problem 3.** **Answer:** Option c: $1$.

**Problem 4.** **Answer:** Option b: $\tan^2 \theta\sec^2 \theta$.

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

**Problem 6.** **Answer:** Option a: $1$.

**Problem 7.** **Answer:** Option d: $\displaystyle\frac{25}{4}$.

**Problem 8.** **Answer:** Option c: $\cos 2\theta$.

**Problem 9.** **Answer:** Option d: $\displaystyle\frac{\sin y}{\sin x}$.

**Problem 10.** **Answer:** Option d: $\text{cot }2\theta$.

### 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.**