waecmaths question:
Given that $\cos x=\tfrac{12}{13}$evaluate $\frac{1-\tan x}{\tan x}$
Option A:
$\tfrac{5}{13}$
Option B:
$\tfrac{5}{7}$
Option C:
$\tfrac{7}{5}$
Option D:
$\tfrac{13}{5}$
waecmaths solution:
$\begin{align} & \text{The pythagoreans triplean }\!\!\{\!\!\text{ 5,12,13 }\!\!\}\!\!\text{ } \\ & opposite=5 \\ & \cos x=\tfrac{12}{13}=\tfrac{adj}{hyp} \\ & \tan x=\tfrac{opp}{adj}=\tfrac{5}{12} \\ & \frac{1-\tan x}{\tan x}=\frac{1-\tfrac{5}{12}}{\tfrac{5}{12}}=\frac{\tfrac{7}{12}}{\tfrac{5}{12}}=\frac{7}{5} \\\end{align}$
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