7th SSC CGL Tier II level Question Set, topic Trigonometry 1
This is the 7th question set of 10 practice problem exercise for SSC CGL Tier II level exam and 1st on topic Trigonometry.
Before taking the test it is recommended that you refer to
Tutorial on Basic and rich concepts in Trigonometry and its applications.
Tutorial on Basic and rich concepts in Trigonometry Part 2, Compound angle functions.
Trigonometry concepts part 3, maxima (or minima) of Trigonometric expressions
Basic and rich algebraic concepts for elegant solutions of SSC CGL problems.
Now set the stopwatch alarm and start taking this test.
7th question set- 10 problems for SSC CGL Tier II exam: 1st on Trigonometry - testing time 15 mins
Problem 1.
If $x=rsin\alpha {cos\beta}$, $y=rsin\alpha{sin\beta}$ and $z=rcos\alpha$, then,
- $x^2-y^2+z^2=r^2$
- $x^2+y^2+z^2=r^2$
- $x^2+y^2-z^2=r^2$
- $y^2+z^2-x^2=r^2$
Problem 2.
With $\angle \theta$ acute, the value of the expression, $\left(\displaystyle\frac{5\ cos \theta - 4}{3-5\ sin \theta} - \displaystyle\frac{3+5\ sin \theta}{4+5\ cos \theta}\right)$ is,
- $1$
- $0$
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{4}$
Problem 3.
If $4+ 3\ tan \alpha=0$, where $\displaystyle\frac{\pi}{2} \lt \alpha \lt \pi$, the value of $2\ cot \alpha - 5\ cos \alpha + \sin \alpha$ is,
- $\displaystyle\frac{23}{10}$
- $-\displaystyle\frac{53}{10}$
- $\displaystyle\frac{37}{10}$
- $\displaystyle\frac{7}{10}$
Problem 4.
If $\ sin \theta + \ sin^2 \theta=1$, then which of the following is true?
- $\ cos \theta +\ cos^2 \theta=1$
- $\ cos^2 \theta +\ cos^3 \theta=1$
- $\ cos^2 \theta +\ cos^4 \theta=1$
- $\ cos \theta -\ cos^2 \theta=1$
Problem 5.
If $a=\sec \theta+\tan \theta$, then $\displaystyle\frac{a^2-1}{a^2+1}$ is,
- $\sec \theta$
- $\cos \theta$
- $\tan \theta$
- $\sin \theta$
Problem 6.
The value of $\displaystyle\frac{cot \theta + cosec \theta - 1}{cot \theta -cosec \theta +1}$ is,
- $cosec \theta - cot \theta$
- $cosec \theta + cot \theta$
- $sec \theta + cot \theta$
- $cosec \theta + tan \theta$
Problem 7.
If $\displaystyle\frac{sin \theta + cos \theta}{sin \theta - cos \theta}=3$, then the value of $sin^4 \theta -cos^4 \theta$ is,
- $\displaystyle\frac{2}{5}$
- $\displaystyle\frac{1}{5}$
- $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{3}{5}$
Problem 8.
If $asec \theta+btan \theta +c=0$, and $psec \theta +qtan \theta +r=0$, then the value of $(br-qc)^2-(pc-ar)^2$ is,
- $(aq+bp)^3$
- $(aq-bp)^3$
- $(aq+bp)^2$
- $(aq-bp)^2$
Problem 9.
If $\alpha + \beta + \gamma=\pi$, then the value of $(sin^2 \alpha + sin^2 \beta - sin^2 \gamma)$ is,
- $2sin \alpha{sin \beta}cos \gamma$
- $2sin \alpha$
- $2sin \alpha{cos \beta}sin \gamma$
- $2sin \alpha{sin \beta}sin \gamma$
Problem 10.
If $sin\alpha sin\beta-cos\alpha cos\beta + 1=0$, then the value of $cot\alpha tan\beta$ is,
- $-1$
- $1$
- $0$
- None of these
The answers are given below, but you will find the detailed conceptual solutions to these questions in SSC CGL Tier II level Solution Set 7 on Trigonometry 1.
If you wish, you may watch the two-part video solutions below.
Part 1: Q1 to Q5
Part 2: Q6 to Q10
Answers to the problems
Problem 1. Answer: b: $x^2+y^2+z^2=r^2$.
Problem 2. Answer: b: 0.
Problem 3. Answer: a: $\displaystyle\frac{23}{10}$.
Problem 4. Answer: c: $cos^2\theta + cos^4\theta=1$
Problem 5. Answer: d: $sin \theta$.
Problem 6. Answer: b: $cosec \theta + cot \theta$.
Problem 7. Answer: d: 1.
Problem 8. Answer: d: $(aq-bp)^2$.
Problem 9. Answer: a: $2sin\alpha sin\beta cos \gamma$.
Problem 10. Answer: a: $-1$.
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