Question:
If $\tan \theta=\frac{4}{3}$ then $(\sin \theta+\cos \theta)=?$
(a) $\frac{7}{3}$
(b) $\frac{7}{4}$
(c) $\frac{7}{5}$
(d) $\frac{5}{7}$
Solution:
Given : $\tan \theta=\frac{4}{3}$
Since, $\tan \theta=\frac{P}{B}$
$\Rightarrow P=4$ and $B=3$
Using Pythagoras theorem,
$P^{2}+B^{2}=H^{2}$
$\Rightarrow 4^{2}+3^{2}=H^{2}$
$\Rightarrow H^{2}=16+9$
$\Rightarrow H^{2}=25$
$\Rightarrow H=5$
Therefore,
$\sin \theta=\frac{P}{H}=\frac{4}{5}$
$\cos \theta=\frac{B}{H}=\frac{3}{5}$
Now,
$\sin \theta+\cos \theta=\frac{4}{5}+\frac{3}{5}$
$=\frac{7}{5}$
Hence, the correct option is (c).