SSC CGL level Question Set 82, Trigonometry 8 | SureSolv

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SSC CGL level Question Set 82, Trigonometry 8

82nd SSC CGL level Question Set, Trigonometry 8

ssc cgl level question set 82 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 as well as the tutorial on powerful alegraic concepts for elegant solutions,

Basic and rich Trigonometry concepts and applications.

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


82nd question set—10 problems for SSC CGL exam: 8th on Trigonometry—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,

  1. $\displaystyle\frac{5}{7}$
  2. $\displaystyle\frac{\sqrt{31}}{5}$
  3. $1$
  4. $\displaystyle\frac{5}{4}\sqrt{\displaystyle\frac{31}{42}}$

Problem 2.

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

  1. $\displaystyle\frac{\sec \theta}{\sec \theta -1}+\displaystyle\frac{\sec \theta}{\sec \theta+1}$
  2. $\displaystyle\frac{\text{cosec } \theta}{\text{cosec } \theta-1}+\displaystyle\frac{\text{cosec } \theta}{\text{cosec } \theta+1}$
  3. $\displaystyle\frac{\text{cosec } \theta}{\sec \theta-1}+\displaystyle\frac{\text{cosec } \theta}{\sec \theta+1}$
  4. $\displaystyle\frac{\sec \theta}{\text{cosec } \theta-1}+\displaystyle\frac{\sec \theta}{\text{cosec } \theta+1}$

Problem 3.

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

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

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,

  1. $\displaystyle\frac{1}{\sqrt{3}}$
  2. $0$
  3. $\sqrt{3}$
  4. $1$

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,

  1. $0$
  2. $1$
  3. $-1$
  4. $2$

Problem 6.

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

  1. $\text{cot } \beta$
  2. $\tan \beta$
  3. $\text{cot } 2\beta$
  4. $\text{cot } \displaystyle\frac{\beta}{2}$

Problem 7.

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

  1. $\sec \theta+\tan \theta$
  2. $\sin \theta\cos \theta$
  3. $\displaystyle\frac{1-\cos \theta}{1+\cos \theta}$
  4. $\displaystyle\frac{1-\sin \theta}{1+\sin \theta}$

Problem 8.

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

  1. $2\tan^2 \theta$
  2. $\sin^2 \theta+\tan^2 \theta$
  3. $\sin^2 \theta\tan^2 \theta$
  4. $2\sin^2 \theta$

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. $-1$
  2. $2$
  3. $0$
  4. $1$

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. $1$
  2. $0$
  3. $-2$
  4. $-1$

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: $1$.


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,

Reading and Practice Guide on Trigonometry in Suresolv for SSC CHSL, SSC CGL, SSC CGL Tier II Other Competitive exams.

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