Question

$\cot \theta =\frac{4}{3}$, evaluate $\frac{4\sin \theta +3\cos \theta }{4\sin \theta -3\cos \theta }$.

Answer 1

$\cot \theta =\frac{4}{3}$

Now, $\frac{4\sin \theta +3\cos \theta }{4\sin \theta -3\cos \theta }=\frac{\sin \theta (4+\frac{3\cos \theta }{\sin \theta })}{\sin \theta (4-\frac{3\cos \theta }{\sin \theta })}$

$=\frac{4+3\cot \theta }{4-3\cot \theta }$

$=\frac{4+3\times \frac{4}{3}}{4-3\times \frac{4}{3}}$

$=\frac{4+4}{4-4}$

$=\frac{8}{0}$

$=$ undefined

Hence, the answer is undefined.