Correct Answer: Option C

Explanation

Given \(\cos x = -\frac{5}{13}\) where \(180^\circ < x < 270^\circ\):

Using: \(\sin^2 x + \cos^2 x = 1\)

\(\sin^2 x = 1 - \left(-\frac{5}{13}\right)^2 = \frac{144}{169} \implies \sin x = -\frac{12}{13}\)

\(\tan x = \frac{\sin x}{\cos x} = \frac{-\frac{12}{13}}{-\frac{5}{13}} = \frac{12}{5}\)

Calculating \(\tan x - \sin x\):

\(\tan x - \sin x = \frac{12}{5} - \left(-\frac{12}{13}\right) = \frac{12}{5} + \frac{12}{13}\)

Finding a common denominator (65):

\(\tan x - \sin x = \frac{12 \times 13}{65} + \frac{12 \times 5}{65} = \frac{156}{65} + \frac{60}{65} = \frac{216}{65}\)

Thus, the value is:

\(\tan x - \sin x = \frac{216}{65}\)

• when will waec gce registration close and how much is it for 2026? Answer this

  1 Answers   ·   1 day ago
• when is mop up exam starting? Answer this

  2 Answers   ·   4 days ago
• if my aggregate is 65 percent can I study economic in lasu? Answer this

  1 Answers   ·   1 day ago