Question : If $\operatorname{cosec} \theta+\cot \theta=2$, then what is the value of $\operatorname{cosec} \theta$?
Option 1: $\frac{5}{4}$
Option 2: $\sqrt{2}$
Option 3: $\sqrt{5}$
Option 4: $\frac{3}{2}$
Correct Answer: $\frac{5}{4}$
Solution :
We know that,
$\operatorname{cosec}^2\theta-\operatorname{cot}^2\theta=(\operatorname{cosec}\theta-\operatorname{cot}\theta)(\operatorname{cosec}\theta+\operatorname{cot}\theta)=1$
$⇒(\operatorname{cosec}\theta-\operatorname{cot}\theta)=\frac{1}{2}$ ----------------(1)
Given,
$\operatorname{cosec} \theta+\cot \theta=2$ ------------------(2)
Solving the above equations, we get,
$\operatorname{cosec} \theta=\frac{5}{4}$
Hence, the correct answer is $\frac{5}{4}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
