Question

If cos$\theta =\frac{2}{3}and\theta$ is in the 4th quadrant, then
$\frac{sin\theta +tan\theta }{sin\theta -tan\theta }$is equal to

• A. $-\frac{1}{5}$
• B. $\frac{1}{5}$
• C. $-5$
• D. $5$

Answer 1

The correct option is C $-5$

$cos\theta =2/3$
$[sin\theta {]}^2+[cos\theta {]}^2=1$
Therefore $sin\theta =-\sqrt{1-\left(2/3\right){}^2}=-\sqrt{5}/3$ ...($\theta$ is in fourth quadrant)
$tan\theta =-\frac{\sqrt{5}}{2}$
Therefore putting in the expression we get
$\frac{-\frac{\sqrt{5}}{3}-\frac{\sqrt{5}}{2}}{-\frac{\sqrt{5}}{3}+\frac{\sqrt{5}}{2}}$
$=-5$
Hence answer is C