If sec x - tan x = 2/3, the tan x = - Path Finder Classes, Chapra

Question

\[ \text{If } \sec x-\tan x=\frac23, \]

\[ \text{then } \tan x=\ ? \]

Using identity

\[ (\sec x+\tan x)(\sec x-\tan x)=1 \]

\[ (\sec x+\tan x)\times\frac23=1 \]

\[ \sec x+\tan x=\frac32 \]

Now,

\[ 2\tan x = (\sec x+\tan x)-(\sec x-\tan x) \]

\[ =\frac32-\frac23 \]

\[ =\frac{9-4}{6} =\frac56 \]

Therefore,

\[ \tan x=\frac5{12} \]

\[ \boxed{\frac5{12}} \]

Spread the love