If tanθ=34 tan ⁡ θ = 3 4 , find the value of sinθ+cosθ sin ⁡ θ + cos ⁡ θ .

If tanθ=34 $\tan \theta =\frac{3}{4}$, find the value of sinθ+cosθ $\sin \theta +\cos \theta$.

Answer Details

tanθ=oppadj=34 $\tan \theta =\frac{opp}{adj}=\frac{3}{4}$

hyp2=opp2+adj2 $hy{p}^2=op{p}^2+ad{j}^2$

hyp=32+42−−−−−−√ $hyp=\sqrt{3^2+4^2}$

= 5

sinθ=35;cosθ=45 $\sin \theta =\frac{3}{5};\cos \theta =\frac{4}{5}$

sinθ+cosθ=35+45 $\sin \theta +\cos \theta =\frac{3}{5}+\frac{4}{5}$

= 75=125