If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)

Explanation

y\(^2\) = 3\(^2\) + 4\(^2\)

y\(^2\) = 9 + 16 

y = \(\sqrt{25}\) 

= 5

\(\frac{\cos x}{2 \sin x} = \frac{4}{5} + 2 \times \frac{3}{5}\)

= \(\frac{4}{5} \times \frac{5}{6}\)

= \(\frac{2}{3}\)