Question:
If $\sec x-\tan x=\frac{2}{3}$, then $\tan x=$ _____________ ,
Solution:
Given $\sec x-\tan x=\frac{2}{3}$ .....(1)
Since $\sec ^{2} x-\tan ^{2} x=1$
$\Rightarrow(\sec x-\tan x)(\sec x+\tan x)=1$
$\Rightarrow \frac{2}{3}(\sec x+\tan x)=1$
$\Rightarrow \sec x+\tan x=\frac{3}{2}$ ....(2)
Subtracting (1) from (2)
$\sec x+\tan x-\sec x+\tan x=\frac{3}{2}-\frac{2}{3}$
$\Rightarrow 2 \tan x=\frac{9-4}{6}$
$\Rightarrow 2 \tan x=\frac{5}{6}$
$\Rightarrow \tan x=\frac{5}{12}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.