Question

If $\theta$ lies in the second quadrant and $tan\theta =\frac{-5}{12}$, find the value of $\frac{2cos\theta }{1-sin\theta }$

Answer 1

$Hypotenus{e}^2$ $=$ $5^2+{12}^2$

$Hypotenuse=13$

$\tan \theta =\frac{-5}{12}$

$\cos \theta =\frac{-12}{13}$ ($\theta$ lies in second quadrant)

$\sin \theta =\frac{5}{13}$

$\frac{2\cos \theta }{1-\sin \theta }=\frac{2\times \frac{-12}{13}}{1-\frac{5}{13}}=\frac{\frac{-24}{13}}{\frac{8}{13}}=-3$