waecmaths question:
If $\tan x=\tfrac{4}{3}$, $0{}^\circ <x<90{}^\circ $, find the value of $\sin x-\cos x$
Option A:
$\tfrac{1}{10}$
Option B:
$\tfrac{1}{5}$
Option C:
$\tfrac{5}{12}$
Option D:
$1\tfrac{2}{5}$
waecmaths solution:
$\begin{align} & \tan x=\tfrac{4}{3}=\tfrac{opp}{adj} \\ & hyp=\sqrt{{{3}^{2}}+{{4}^{2}}}=5 \\ & \sin x=\tfrac{opp}{hyp}=\tfrac{4}{5} \\ & \cos x=\tfrac{adj}{hyp}=\tfrac{3}{5} \\ & \sin x-\cos x=\tfrac{4}{5}-\tfrac{3}{5}=\tfrac{1}{5} \\\end{align}$
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