Question 27

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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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