Question : If $\sec ^2 \mathrm{~A}+\tan ^2 \mathrm{~A}=3$, then what is the value of $\cot \mathrm{A}$?
Option 1: $\frac{1}{\sqrt{3}}$
Option 2: $0$
Option 3: $1$
Option 4: $\sqrt{3}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: $1$
Solution :
Given: $\sec ^2\mathrm{A}+\tan ^2 \mathrm{A}=3$
⇒ $\frac{1}{\cos^2 \mathrm{A}} + \frac{\sin^2\mathrm{A}}{\cos^2\mathrm{A}} = 3$
⇒ $1+\sin^2\mathrm{A} = 3\cos^2\mathrm{A}$
⇒ $\sin^\mathrm{A} + \cos^2\mathrm{A} + \sin^2\mathrm{A} = 3 \cos^2\mathrm{A}$
⇒ $2\sin^2\mathrm{A} = 2\cos^2\mathrm{A}$
⇒ $\frac{\sin^2\mathrm{A}}{\cos^2\mathrm{A}} = 1$
⇒ $\tan^2\mathrm{A} = 1$
⇒ $\tan\mathrm{A} = 1$
$\therefore$ $\cot\mathrm{A} = 1$
Hence, the correct answer is 1.
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 “”.
