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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