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SSC CGL Tier II level Question Set 11, Trigonometry 2

Submitted by Atanu Chaudhuri on Sat, 26/05/2018 - 23:44

SSC CGL Tier 2 Trigonometry Questions Set 11

SSC CGL Tier 2 Question Set 11 on Trigonometry with answers

Solve 10 selected questions in SSC CGL Tier 2 trigonometry questions set 11 in 12 minutes. Verify results from given answers. Learn to solve from solutions.

Answers and linked solution set are at the end.

SSC CGL Tier 2 Trigonometry Questions set 11 - testing time 12 mins

Problem 1.

If $5 cos \theta +12 sin \theta=13$, and $0^0 \lt \theta \lt 90^0$, then the value of $\sin \theta$,

  1. $-\displaystyle\frac{12}{13}$
  2. $\displaystyle\frac{12}{13}$
  3. $\displaystyle\frac{5}{13}$
  4. $\displaystyle\frac{6}{13}$

Problem 2.

The value of $(cosec \theta -sin \theta)(sec \theta - cos \theta)(tan \theta +cot \theta)$ is,

  1. 1
  2. 2
  3. 4
  4. 6

Problem 3.

If $tan A = n tan B$ and $sin A = m sin B$, then the value of $cos^2 A$ is,

  1. $\displaystyle\frac{m^2+1}{n^2-1}$
  2. $\displaystyle\frac{m^2+1}{n^2+1}$
  3. $\displaystyle\frac{m^2 -1}{n^2+1}$
  4. $\displaystyle\frac{m^2 -1}{n^2-1}$

Problem 4.

If $\theta$ is a positive acute angle and $3(sec^2 \theta + tan^2 \theta)=5$, then the value of $cos 2\theta$ is,

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

Problem 5.

If $tan \alpha = 2$, then the value of $\displaystyle\frac{cosec^2 \alpha - sec^2 \alpha}{cosec^2+sec^2 \alpha}$ is,

  1. $-\displaystyle\frac{3}{5}$
  2. $-\displaystyle\frac{15}{9}$
  3. $\displaystyle\frac{17}{5}$
  4. $\displaystyle\frac{3}{5}$

Problem 6.

If $\sin (\theta + 30^0)=\displaystyle\frac{3}{\sqrt{2}}$ the value of $cos^2 \theta$ is,

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

Problem 7.

$(1 + sec 20^0 + cot 70^0)(1 - cosec 20^0 + tan 70^0)$ is equal to,

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

Problem 8.

If $tan \theta - cot \theta =0$, and $\theta$ is a positive acute angle, then the value of $\displaystyle\frac{tan (\theta+15^0)}{tan(\theta-15^0)}$ is,

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

Problem 9.

If $sec \theta - tan \theta=\displaystyle\frac{1}{\sqrt{3}}$, then the value of $sec \theta.tan \theta$ is,

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

Problem 10.

If $tan (5x - 10^0)=cot (5y+20^0)$, then the value of $x+y$ is,

  1. $15^0$
  2. $16^0$
  3. $20^0$
  4. $24^0$

Answers to SSC CGL Tier 2 Trigonometry Questions set 11

Problem 1. Answer: b: $\displaystyle\frac{12}{13}$.

Problem 2. Answer: a: 1.

Problem 3. Answer: d: $\displaystyle\frac{m^2-1}{n^2-1}$.

Problem 4. Answer: c: $\displaystyle\frac{1}{2}$

Problem 5. Answer: a: $-\displaystyle\frac{3}{5}$.

Problem 6. Answer: c: $\displaystyle\frac{3}{4}$.

Problem 7. Answer: d: 2.

Problem 8. Answer: a: 3.

Problem 9. Answer: a: $\displaystyle\frac{2}{3}$.

Problem 10. Answer: b: $16^0$.

For detailed conceptual solutions please refer to companion SSC CGL Tier II level solution set 11 Trigonometry 2.

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