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If tan x = $\frac{3}{4}$ , 0 < x < 90 $^o$ , evaluate...

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.

$\frac{2}{3}$

View answer & explanation

Correct answer is D

y $^2$ = 3 $^2$ + 4 $^2$

y $^2$ = 9 + 16

y = $\sqrt{25}$

= 5

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

= $\frac{4}{5} \times \frac{5}{6}$

= $\frac{2}{3}$

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