Question : If $\sin \theta=\frac{8}{17}$, where $\theta$ is an acute angle, then what is the value of $\tan \theta+\cot \theta ?$
Option 1: $\frac{217}{110}$
Option 2: $\frac{281}{190}$
Option 3: $\frac{289}{120}$
Option 4: $\frac{512}{321}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: $\frac{289}{120}$
Solution :
Given, $\sin \theta=\frac{8}{17}$
We know that $\sin^2 \theta + \cos^2 \theta=1$.
So, $(\frac{8}{17})^2+ \cos^2 \theta=1$
$⇒\cos^2 \theta = 1 - \frac{64}{289}$
$⇒\cos^2 \theta = \frac{225}{289}$
$⇒\cos \theta = \frac{15}{17}$
Now, $\tan \theta+\cot \theta = \frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}$
$⇒\tan \theta+\cot \theta = \frac{\sin^2 \theta + \cos^2 \theta}{\sin \theta\cos \theta}$
$⇒\tan \theta+\cot \theta = \frac{1}{\frac{8}{17}\times \frac{15}{17}}$
$⇒\tan \theta+\cot \theta = \frac{289}{120}$
Hence, the correct answer is $\frac{289}{120}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
