Question : Which of the following is equal to $[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$?
Option 1: $\operatorname{cosec} \theta \sec \theta$
Option 2: $\sec \theta\tan \theta$
Option 3: $\operatorname{cosec} \theta\tan \theta$
Option 4: $\cot \theta \sec \theta$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: $\operatorname{cosec} \theta \sec \theta$
Solution :
Given: The expression is $[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$.
We know the trigonometric ratios, $\frac{1}{\sin \theta} =\operatorname{cosec} \theta$ and $\frac{1}{\cos \theta} = \sec \theta$ and the trigonometric identity, $\sin^2\theta+\cos^2\theta=1$
$[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$
$=\frac{\sin^2\theta+\cos^2\theta}{\sin \theta\times \cos \theta}$
$=\frac{1}{\sin \theta\times \cos \theta}=\operatorname{cosec} \theta \sec \theta$
Hence, the correct answer is $\operatorname{cosec} \theta \sec \theta$.
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 “”.
