If cos x = - \(\frac{5}{13}\) where 180° < X < 270°, what is the value of tan x -sin x ?

A.

\(\frac{111}{13}\)

B.

\(\frac{321}{65}\)

C.

-\(\frac{216}{65}\)

D.

\(\frac{112}{13}\)

E.

\(\frac{131}{65}\)

Correct answer is C

Given  cos x = - \(\frac{5}{13}\) 

→ adj = -5, hyp = 13 

Pythagoras' rule → hyp\(^2\) = Opp\(^2\) + adj\(^2\)

Opp\(^2\) = 13\(^2\) - [-5]\(^2\) → 169 - 25

Opp = √144 → 12

tan x = \(\frac{opp}{adj}\) → - \(\frac{12}{5}\) 

sin x = \(\frac{opp}{hyp}\) → \(\frac{12}{13}\) 

; tan x - sin x →  - \(\frac{12}{5}\) -  \(\frac{12}{13}\) 

=  - \(\frac{216}{65}\)