If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
A
\(\frac{8}{3}\)
B
\(\frac{3}{2}\)
C
\(\frac{4}{3}\)
D
\(\frac{2}{3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
y\(^2\) = 3\(^2\) + 4\(^2\)
y\(^2\) = 9 + 16
y = \(\sqrt{25}\)
= 5
\(\frac{\cos x}{2 \sin x} = \frac{4}{5} + 2 \times \frac{3}{5}\)
= \(\frac{4}{5} \times \frac{5}{6}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #57365)