## Difficult trigonometry questions and answers for SSC CGL: questions to be solved in 12 minutes

10 difficult trigonometry questions and answers for SSC CGL Set 1. Solve in 12 minutes. Verify score from answers. Learn to solve from solutions.

For best results try to solve all the 10 questions within 12 minutes' time. At the end of this period, score your efforts with 1 mark for every correct answer and minus 0.25 for every wrong one.

You will find the **answers at the end of the questions.**

After taking the test go through the solutions carefully to learn how to solve the questions quickly and correctly from the paired solution set. If needed repeat the test again after some time to check how much you have retained.

**Link to the solution set** is also at the end.

Now set your timer on and start.

### Set 1 of 10 Trigonometry difficult questions for competitive exams SSC CGL - time to solve 12 minutes

**Q1.** If $0^0 < \theta < 90^0$ and $2sin^2\theta + 3cos\theta = 3$ then the value of $\theta$ is,

- $30^0$
- $60^0$
- $45^0$
- $75^0$

**Q2.** If $sin\theta=\displaystyle\frac{a}{\sqrt{a^2 + b^2}}$, then the value of $cot\theta$ will be,

- $\displaystyle\frac{b}{a}$
- $\displaystyle\frac{a}{b}$
- $\displaystyle\frac{a}{b} + 1$
- $\displaystyle\frac{b}{a} + 1$

**Q3.** If $tan\theta=\frac{3}{4}$ and $0<\theta<\frac{\pi}{2}$ and $25xsin^2\theta{cos\theta}=tan^2\theta$, then the value of $x$ is,

- $\frac{7}{64}$
- $\frac{9}{64}$
- $\frac{3}{64}$
- $\frac{5}{64}$

**Q4.** If $xsin\theta - ycos\theta = \displaystyle\sqrt{x^2 + y^2}$ and $\displaystyle\frac{cos^2\theta}{a^2} + \frac{sin^2\theta}{b^2} = \frac{1}{x^2 + y^2}$ then,

- $\displaystyle\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$
- $\displaystyle\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
- $\displaystyle\frac{x^2}{b^2} - \frac{y^2}{a^2} = 1$

**Q5.** The value of $sin^21^0+sin^23^0+sin^25^0+...$

$...+sin^287^0+sin^289^0$ is,

- $22$
- $22\frac{1}{2}$
- $23$
- $22\frac{1}{4}$

**Q6.** The minimum value of $cos^2\theta + sec^2\theta$ is,

- 0
- 1
- 2
- 3

**Q7.** If $cos\theta + sec\theta = 2$ $(0^0\leq{\theta}\leq{90^0})$ then the value of $cos{10}\theta + sec{11}\theta$ is,

- 0
- 1
- 2
- -1

**Q8.** If $tan\theta=\frac{3}{4}$ and $\theta$ is acute then, $cosec\theta$ is equal to,

- $\frac{5}{3}$
- $\frac{5}{4}$
- $\frac{4}{3}$
- $\frac{4}{5}$

**Q9.** If $\displaystyle\frac{sin\theta + cos\theta}{sin\theta - cos\theta} = 3$ then the numerical value of $sin^4\theta - cos^4\theta$ is,

- $\frac{1}{2}$
- $\frac{2}{5}$
- $\frac{3}{5}$
- $\frac{4}{5}$

**Q10.** The minimum value of $2sin^2\theta + 3cos^2\theta$ is,

- 0
- 3
- 2
- 1

Learn how to solve the questions in 12 minutes or less from the paired solution set,

**SSC CGL level Solution Set 2 on Trigonometry.**

### Answers to the 10 Trigonometry difficult questions for competitive exams SSC CGL Set 1

**Problem 1. Answer:** Option b: $60^0$.

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

**Problem 3. Answer:** Option d: $\frac{5}{64}$.

**Problem 4. Answer:** Option b: $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$.

**Problem 5. Answer:** Option b: $22\frac{1}{2}$.

**Problem 6. Answer:** Option c : 2.

**Problem 7. Answer:** Option c: 2.

**Problem 8. Answer:** Option a: $\frac{5}{3}$.

**Problem 9. Answer:** Option c: $\frac{3}{5}$.

**Problem 10. Answer:** Option c: 2.

### Guided help on Trigonometry in Suresolv

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