Question 34

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Jambmaths question: 

In a right angle triangle, if tan θ = ¾ what is cos θsin θ

Jamb Maths Solution: 

$\begin{align}  & \tan \theta =\frac{3}{4} \\ & \text{By definition }\tan \theta =\frac{opposite}{adjacent} \\ & \text{Using pythagoras theorem} \\ & hypotenu{{s}^{2}}={{3}^{2}}+{{4}^{2}} \\ & hypotenu{{s}^{2}}=25 \\ & hypotenus=5 \\ & \sin \theta =\frac{opp}{hyp}=\frac{3}{5} \\ & \cos \theta =\frac{adj}{hyp}=\frac{4}{5} \\ & \cos \theta -\sin \theta =\frac{4}{5}-\frac{3}{5}=\frac{1}{5} \\\end{align}$

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