SSC CGL level Question Set 56, Trigonometry 5

Solve Trigonometry Aptiude questions with answers for SSC CGL Set 56

Solve 10 trigonometry aptitude questions for SSC CGL Set 56 in 12 minutes. Verify correctness from answers and learn to solve from paired solutions.

Answers and link to the solutions are at the end.

Now set the timer on and take the test like an actual test.

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10 Trigonometry aptitude questions for SSC CGL Set 56 - time to solve 12 mins

Problem 1.

The maximum value of $(2\sin \theta + 3\cos\theta)$ is,

1. $1$
2. $2$
3. $\sqrt{13}$
4. $\sqrt{15}$

Problem 2.

Find the minimum value of $9\tan^2 \theta + 4\cot^2 \theta$,

1. $15$
2. $6$
3. $9$
4. $12$

Problem 3.

If $\text{cosec} \theta -\cot \theta= \displaystyle\frac{7}{2}$, the value of $\text{cosec} \theta$ is,

1. $\displaystyle\frac{49}{28}$
2. $\displaystyle\frac{53}{28}$
3. $\displaystyle\frac{47}{28}$
4. $\displaystyle\frac{51}{28}$

Problem 4.

If $\tan^2 \alpha=1 +2\tan^2 \beta$, where $\alpha$ and $\beta$ both are positive acute angles, find the value of $\sqrt{2}\cos \alpha - \cos \beta$.

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

Problem 5.

The value of $152(\sin 30^0 + 2\cos^2 45^0 + 3\sin 30^0 +$

$\hspace{30mm}4\cos^2 45^0 + ....+17\sin 30^0+18\cos^2 45^0)$ is,

1. an irrational number
2. a rational number but not an integer
3. an integer but not a perfect square
4. the perfect square of an integer

Problem 6.

If $\tan \theta + \cot \theta=2$, then the value of $\tan^n \theta + \cot^n \theta$ ($0^0 \lt \theta \lt 90^0$, and $n$ an integer) is,

1. $2$
2. $2^{n+1}$
3. $2^n$
4. $2n$

Problem 7.

If $\displaystyle\frac{\sin \theta}{1+\cos \theta} + \displaystyle\frac{\sin \theta}{1-\cos \theta} = 4$, the value of $\cot \theta + \sec \theta$ is,

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

Problem 8.

If $\sin \theta + \cos \theta =\sqrt{2}$ with $\angle \theta$ a positive acute angle, then the value of $\tan \theta + \sec \theta$ is,

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

Problem 9.

If $p=a\sec {\theta}\cos \alpha$, $q =b\sec {\theta}\sin \alpha$, and $r =c\tan \theta$, then the value of $\displaystyle\frac{p^2}{a^2} +\displaystyle\frac{q^2}{b^2}-\displaystyle\frac{r^2}{c^2}$ is,

1. 0
2. 1
3. 4
4. 5

Problem 10.

$\displaystyle\frac{\sin^2 \theta}{\cos^2 \theta}+\displaystyle\frac{\cos^2 \theta}{\sin^2 \theta}$ 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. $\displaystyle\frac{\sin^2 \theta}{\cot \theta - \sec \theta}$

Conceptual and quick solution of the questions is at,

SSC CGL Solution set 56 on Trigonometry.

For trigonometry concepts read,

Basic and rich trigonometry concepts and application.

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Answers to the 10 Trigonometry aptitude questios for SSC CGL Set 56

Problem 1. Answer: c: $\sqrt{13}$.

Problem 2. Answer: d: $12$.

Problem 3. Answer: b: $\displaystyle\frac{53}{28}$.

Problem 4. Answer: a: $0$.

Problem 5. Answer: d: the perfect square of an integer.

Problem 6. Answer: a: $2$.

Problem 7. Answer: d: $\displaystyle\frac{5}{\sqrt{3}}$.

Problem 8. Answer: b: $\displaystyle\frac{1}{\sqrt{2}-1}$.

Problem 9. Answer: b: 1.

Problem 10. Answer: b: $\displaystyle\frac{1}{\sin^2 {\theta}\cos^2 \theta}-2$.

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