Question

If $4\tan \theta =3$ evaluate $\frac{4\sin \theta -\cos \theta +1}{4\sin \theta +\cos \theta -1}$

Answer 1

It is given that,

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

So, $cos\theta =\frac{4}{5}$ and $sin\theta =\frac{3}{5}$

Hence, $\frac{4sin\theta -cos\theta +1}{4sin\theta +cos\theta -1}$

$⟹\frac{4\times \frac{3}{5}-\frac{4}{5}+1}{4\times \frac{3}{5}+\frac{4}{5}-1}$

$⟹\frac{\frac{13}{5}}{\frac{11}{5}}$

$⟹\frac{13}{11}$