SSC CGL Tier II level Question Set 12 Trigonometry 3, questions with answers

Trigonometry questions for competitive exams with answers

Solve 10 selected Trigonometry questions for SSC CGL Tier 2 Set 12 in 12 minutes. Verify your score from answers and learn to solve quickly from solutions.

The answers to the questions and link to the detailed solutions are given at the end.

---

10 selected Trigonometry questions for SSC CGL Tier 2 Set 12 - time to answer 12 mins

Problem 1.

If $2abcos \theta + (a^2-b^2)sin \theta=a^2+b^2$ then the value of $tan \theta$ is,

1. $\displaystyle\frac{1}{2ab}(a^2+b^2)$
2. $\displaystyle\frac{1}{2}(a^2-b^2)$
3. $\displaystyle\frac{1}{2}(a^2+b^2)$
4. $\displaystyle\frac{1}{2ab}(a^2-b^2)$

Problem 2.

$\displaystyle\frac{\sin^2 \theta}{\cos^2 \theta}+\displaystyle\frac{\cos^2 \theta}{\sin^2 \theta}$ is equal to,

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

Problem 3.

If $cos \theta + sec \theta = 2$, then the value of $cos^5 \theta + sec^5 \theta$ is,

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

Problem 4.

$sin(\alpha + \beta -\gamma)=cos(\beta + \gamma -\alpha)=\displaystyle\frac{1}{2}$ and $tan(\gamma + \alpha -\beta)=1$. If $\alpha$, $\beta$ and $\gamma$ are positive acute angles, value of $2\alpha + \beta$ is,

1. $105^0$
2. $110^0$
3. $115^0$
4. $120^0$

Problem 5.

If $sin \theta + sin^2 \theta=1$, then the value of $cos^{12} \theta + 3cos^{10} \theta + 3cos^{8} \theta + cos^6 \theta - 1$ is,

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

Problem 6.

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

1. 4
2. 0
3. 2
4. 1

Problem 7.

If $4cos^2 \theta - 4\sqrt{3}cos \theta + 3=0$ and $0^0 \leq \theta \leq 90^0$, then the value of $\theta$ is,

1. $60^0$
2. $90^0$
3. $30^0$
4. $45^0$

Problem 8.

If $sin \theta + cos \theta=\sqrt{2}sin(90^0 - \theta)$ then the value of $cot \theta$ is,

1. $\sqrt{2}-1$
2. $\sqrt{2}+1$
3. $-\sqrt{2}+1$
4. $-\sqrt{2}-1$

Problem 9.

If $x=asin \theta-bcos \theta$ and $y=acos \theta + bsin \theta$, then which of the following is true?

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

Problem 10.

If $tan \theta=\displaystyle\frac{a}{b}$, then the value of $\displaystyle\frac{asin^3 \theta - bcos^3 \theta}{asin^3 \theta + bcos^3 \theta}$ is,

1. $\displaystyle\frac{a^4-b^4}{a^4+b^4}$
2. $\displaystyle\frac{a^3+b^3}{a^3-b^3}$
3. $\displaystyle\frac{a^3-b^3}{a^3+b^3}$
4. $\displaystyle\frac{a^4+b^4}{a^4-b^4}$

To know how to solve the questions quickly go through the paired solution set at,

SSC CGL Tier II Solution set 12 Trigonometry 3, questions with solutions.

---

Answers to the Trigonometry questions for SSC CGL Tier 2 Set 12

Problem 1. Answer: Option d: $\displaystyle\frac{1}{2ab}(a^2-b^2)$.

Problem 2. Answer: Option b: $\displaystyle\frac{1}{\sin^2 \theta.cos^2 \theta} -2$.

Problem 3. Answer: Option b: $2$.

Problem 4. Answer: Option d: $120^0$.

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

Problem 6. Answer: Option c: 2.

Problem 7. Answer: Option c: $30^0$.

Problem 8. Answer: Option b: $\sqrt{2}+1$.

Problem 9. Answer: Option a: $x^2 + y^2=a^2 + b^2$.

Problem 10. Answer: Option a: $\displaystyle\frac{a^4-b^4}{a^4+b^4}$.

---

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.

The guide list of articles is up-to-date.

---