Difficult Trigonometry Question Set 18 SSC CGL Tier 2 with answers
Solve 10 difficult trigonometry questions for SSC CGL Tier 2 Set 18 in 12 minutes. Verify from answers. Learn how to solve quickly from paired solutions.
Recommendation
Before taking the test you should refer to the tutorials on,
Basic and rich concepts in Trigonometry and its applications, and,
Basic and rich algebraic concepts for elegant solutions of SSC CGL problems.
The test should be used as a mini-mock test and answering timed with the timer on. When the time is over, don't stop answering. Just mark the point up to which you have answered in the scheduled time and go on to complete the test.
After the test, score yourself on your answer in scheduled time and analyze all the difficulties by going through the corresponding solution set.
Answers and link to the paired solution set are at the end.
Now set the timer on and start taking the test.
10 Difficult Trigonometry Questions for SSC CGL Tier 2 - time to answer 12 mins
Problem 1.
The value of
$\displaystyle\frac{4\cos(90^0- \theta)\sin^3(90^0+\theta)-4\sin(90^0+\theta)\cos^3(90^0-\theta)}{\cos\left(\displaystyle\frac{180^0+8\theta}{2}\right)}$ is,
- $0$
- $-1$
- $1$
- $2$
Problem 2.
If $\sec \theta(\cos \theta+\sin \theta)=\sqrt{2}$ then the value of $\displaystyle\frac{2\sin \theta}{\cos \theta -\sin \theta}$ is equal to,
- $\sqrt{2}$
- $\displaystyle\frac{1}{\sqrt{2}}$
- $3\sqrt{2}$
- $\displaystyle\frac{3}{\sqrt{2}}$
Problem 3.
The value of $\displaystyle\frac{(\sin x+\sin y)(\sin x - \sin y)}{(\cos x+\cos y)(\cos y - \cos x)}$ is,
- $0$
- $2$
- $1$
- $-1$
Problem 4.
The value of $\displaystyle\frac{1}{\sin^4(90^0-\theta)}+\displaystyle\frac{1}{\cos^2(90^0-\theta)-1}$ is,
- $\tan^4 \theta$
- $\tan^2 \theta\sec^2 \theta$
- $\sec^4 \theta$
- $\tan^2 \theta\sin^2 \theta$
Problem 5.
The value of $\sin(B-C)\cos(A-D)$
$\hspace{22mm}+\sin(A-B)\cos(C-D)$
$\hspace{22mm}+\sin(C-A)\cos(B-D)$ is,
- $\displaystyle\frac{3}{2}$
- $0$
- $-3$
- $1$
Problem 6.
The value of $\left[\tan^2(90^0-\theta)-\sin^2(90^0-\theta)\right]$
$\hspace{22mm}\times{\text{cosec}^2(90^0-\theta)\text{cot}^2(90^0-\theta)}$ is,
- $1$
- $0$
- $2$
- $-1$
Problem 7.
The value of $\displaystyle\frac{4}{3}\text{cot}^2\left(\displaystyle\frac{\pi}{6}\right)+3\cos^2(150^0)$
$\hspace{22mm}-4\text{cosec}^245^0+8\sin\left(\displaystyle\frac{\pi}{2}\right)$ is,
- $1$
- $\displaystyle\frac{13}{2}$
- $-\displaystyle\frac{7}{2}$
- $\displaystyle\frac{25}{4}$
Problem 8.
The value of $\displaystyle\frac{\tan 5\theta+\tan 3\theta}{4\cos 4\theta(\tan 5\theta-\tan 3\theta)}$ is,
- $\tan 4\theta$
- $\sin 2\theta$
- $\cos 2\theta$
- $\text{cot }2\theta$
Problem 9.
The value of $\displaystyle\frac{\sin(y-z)+\sin(y+z)+2\sin y}{\sin(x-z)+\sin(x-z)+2\sin x}$ is,
- $\cos x\sin y$
- $\sin x\tan y$
- $\sin z$
- $\displaystyle\frac{\sin y}{\sin x}$
Problem 10.
The value of $\displaystyle\frac{\sin(90^0-10\theta)-\cos(\pi-6\theta)}{\cos\left(\displaystyle\frac{\pi}{2}-10\theta\right)-\sin(\pi-6\theta)}$ is,
- $\cos \theta$
- $\tan 2\theta$
- $\text{cot }3\theta$
- $\text{cot }2\theta$
To know how to solve the questions quickly, go through the paired solution set at,
SSC CGL Tier II Solution Set 18 Trigonometry 4.
Answers to the difficult trigonometry questions for SSC CGL Tier 2 Set 18
Problem 1. Answer: Option b: $-1$.
Problem 2. Answer: Option a: $\sqrt{2}$.
Problem 3. Answer: Option c: $1$.
Problem 4. Answer: Option b: $\tan^2 \theta\sec^2 \theta$.
Problem 5. Answer: Option b: $0$.
Problem 6. Answer: Option a: $1$.
Problem 7. Answer: Option d: $\displaystyle\frac{25}{4}$.
Problem 8. Answer: Option c: $\cos 2\theta$.
Problem 9. Answer: Option d: $\displaystyle\frac{\sin y}{\sin x}$.
Problem 10. Answer: Option d: $\text{cot }2\theta$.
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