Question 33

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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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