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SSC CGL level Question Set 65, Trigonometry 6

Hard trigonometry questions answers for competitive exams

Hard trigonometry questions answers for competitive exams SSC CGL Set 65

Hard trigonometry questions answers for competitive exams SSC CGL 65. Take the timed test, verify from answers and learn to solve in time from solutions..

The link of the solutions is at the end.

After taking the test, scoring and going through the solutions, if needed repeat the test. That'll be a good check on how far you could absorb the techniques and concepts needed to solve these 10 questions comfortably in time.

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Hard trigonometry questions answers for competitive exams SSC CGL Set 65 - testing time 12 mins

Problem 1.

If $2-cos^2 \theta=3sin \theta{cos \theta}$, where $sin \theta \neq cos \theta$, the value of $tan \theta$ is,

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

Problem 2.

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

  1. $\sqrt{2}-1$
  2. $\sqrt{2}+1$
  3. $0$
  4. $\sqrt{2}$

Problem 3.

If $(a^2-b^2)sin \theta + 2abcos \theta=a^2+b^2$ 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 4.

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 5.

If $cot \theta + cosec \theta =3$, and $\theta$ an acute angle, the value of $cos \theta$ is,

  1. $1$
  2. $\displaystyle\frac{1}{2}$
  3. $\displaystyle\frac{4}{5}$
  4. $\displaystyle\frac{3}{4}$

Problem 6.

If $xcos \theta - sin \theta=1$, then the value of $x^2-(1+x^2)sin \theta$ is,

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

Problem 7.

If $\theta=60^0$, then the value of $\displaystyle\frac{1}{2}\sqrt{1+ sin \theta} + \displaystyle\frac{1}{2}\sqrt{1- sin \theta}$ is,

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

Problem 8.

If $3sin \theta + 5cos \theta =5$, ($0\lt \theta \lt 90^0$), then the value of $5sin \theta-3cos \theta$ will be,

  1. 1
  2. 2
  3. 5
  4. 3

Problem 9.

If $tan \theta = \displaystyle\frac{1}{\sqrt{11}}$, and $0\lt \theta \lt 90^0$, then the value of $\displaystyle\frac{cosec^2 \theta - sec^2 \theta}{cosec^2 \theta + sec^2 \theta}$ is,

  1. $\displaystyle\frac{5}{6}$
  2. $\displaystyle\frac{3}{4}$
  3. $\displaystyle\frac{4}{5}$
  4. $\displaystyle\frac{6}{7}$

Problem 10.

If $tan^2 \theta=1-e^2$, then the value of $sec \theta + tan^3 \theta{cosec \theta}$ is equal to,

  1. $(2+e^2)^{\frac{3}{2}}$
  2. $(2+e^2)^{\frac{1}{2}}$
  3. $(2-e^2)^{\frac{3}{2}}$
  4. $(2-e^2)^{\frac{1}{2}}$

The answers are given below.

Learn how to solve the questions in 12 minutes scheduled time from SSC CGL level Solution Set 65 on Trigonometry 6.


Answers to the questions

Problem 1. Answer: b: $\displaystyle\frac{1}{2}$.

Problem 2. Answer: a: $\sqrt{2}-1$.

Problem 3. Answer: d: $\displaystyle\frac{1}{2ab}(a^2-b^2)$.

Problem 4. Answer: Option c: 2.

Problem 5. Answer: c: $\displaystyle\frac{4}{5}$.

Problem 6. Answer: a: $1$.

Problem 7. Answer: b: $cos \displaystyle\frac{\theta}{2}$.

Problem 8. Answer: d: 3.

Problem 9. Answer: a: $\displaystyle\frac{5}{6}$.

Problem 10. Answer: c: $(2-e^2)^{\frac{3}{2}}$.


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