Question : If $\sec \theta-\tan \theta=m$, then $2 \tan \theta=?$
Option 1: $\frac{1-m}{m} \\$
Option 2: $ \frac{1-m^2}{m} \\$
Option 3: $\frac{1+m^2}{m} \\$
Option 4: $ \frac{m^2-1}{m}$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $ \frac{1-m^2}{m} \\$
Solution :
$\sec \theta-\tan \theta=m$ ---(i)
$\sec^2 \theta-\tan ^2\theta=1$
$⇒(\sec \theta-\tan \theta)(\sec \theta+\tan \theta)=1$
$⇒(\sec \theta+\tan \theta)=\frac{1}{(\sec \theta-\tan \theta)}$
$⇒(\sec \theta+\tan \theta)=\frac{1}{m}$ ---(ii)
Subtracting equation (ii) from (i), we get
$⇒-2\tan \theta=m-\frac{1}{m}$
$⇒2\tan \theta=\frac{1}{m}-m$
$⇒2\tan\theta=\frac{1-m^2}{m}$
Hence, the correct answer is $\frac{1-m^2}{m}$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates BrochureYour Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.