Question 34

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Jambmaths question: 

If $\tan \theta =\tfrac{3}{4}$,  find the value of  $\sin \theta +\cos \theta$

Option A: 

$1\tfrac{2}{3}$

Option B: 

$1\tfrac{3}{5}$

Option C: 

$1\tfrac{2}{5}$

Option D: 

$1\tfrac{1}{3}$

Jamb Maths Solution: 

$\begin{align}  & \text{tan}\theta \text{=}\frac{3}{4} \\ & \text{By definition }\tan \theta =\frac{opp}{adj} \\ & \text{using pythagoras theorem } \\ & A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}} \\ & A{{C}^{2}}={{3}^{2}}+{{4}^{2}} \\ & AC=\sqrt{9+16}=5 \\ & \sin \theta =\frac{opp}{hyp}=\frac{AB}{AC}=\frac{3}{5} \\ & \cos \theta =\frac{adj}{hyp}=\frac{BC}{AC}=\frac{4}{5} \\ & \sin \theta +\cos \theta =\frac{3}{5}+\frac{4}{5}=\frac{7}{5}=1\frac{2}{5} \\\end{align}$

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