If $5 \cos \theta=3$, then the value of $\tan \theta-\sec \theta$ is:

$-\frac{1}{3}$

cosθ  = \(\frac{3}{5}\) = \(\frac{B}{H}\)

Now, using pythagoras theorem

H² = P²+ B²

5² = P² + 3²

25 = P² + 9

P² = 16

P = 4

Now, tanθ - secθ

= \(\frac{P}{B}\) - \(\frac{H}{B}\)

= \(\frac{4}{3}\) - \(\frac{5}{3}\)

= - \(\frac{1}{3}\) 

The correct answer is Option (3) → $-\frac{1}{3}$