If $\tan \theta =\frac{-4}{3}$  and  $\theta$  does not lie in the IV quadrant then  $5\sin \theta +10\cos \theta +9\sec \theta +16\cos ec\theta +4\cot \theta =$

$\tan \theta =\frac{-4}{3}$   and $\theta \notin Q_4$  then $\theta \in Q_2$ 

$\sin \theta =\frac{4}{5}$  , $\cos \theta =\frac{-3}{5}$  , $\sec \theta =\frac{-5}{3}$ , $\cos ec\theta =\frac{5}{4}$  , $\cot \theta =\frac{-3}{4}$

$5\sin \theta +10\cos \theta +9\sec \theta +16\cos ec\theta +4\cot \theta =4-6-15+20-3=0.$