Jambmaths question:
In a right angled triangle, if $\tan \theta =\tfrac{3}{4}$ what is $\cos \theta -\sin \theta $?
Option A:
$\tfrac{1}{5}$
Option B:
$\tfrac{2}{5}$
Option C:
$\tfrac{3}{5}$
Option D:
$\tfrac{4}{5}$
Jamb Maths Solution:
$\begin{align} & \text{Using Pythagoras triple the sides of the triangle is 3},\text{ 4},\text{ 5} \\ & \tan \theta =\frac{opp}{adj}=\frac{3}{4} \\ & \sin \theta =\frac{opp}{hyp}=\frac{3}{5} \\ & \cos \theta =\frac{adj}{hyp}=\frac{4}{5} \\ & \cos \theta -\sin \theta =\frac{4}{5}-\frac{3}{5}=\frac{1}{5} \\\end{align}$
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