Hard Trigonometry Questions for SSC CGL Set 82 with Answers
Hard trigonometry questions for SSC CGL Set 82: 10 difficult questions to be solved in 12 mins. Verify from answers. Learn to solve quickly from solutions.
Answer to the questions and link to the paired solution set are at the end.
10 hard Trigonometry questions for SSC CGL Set 82 - testing time 12 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 hard trigonometry questions for SSC CGL Set 82
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: $1$.
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