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. $\frac{5}{7}$

Answer 1

The correct option is C $\frac{7}{5}$

$\tan \theta =\frac{AC}{AB}=\frac{4}{3}=\frac{4x}{3x}\Rightarrow BC=4x$ and $AB=3x$

By Pythagoras theorem,

$A{C}^2=A{B}^2+B{C}^2$
$=16x^2+9x^2$
$=25x^2$
$\therefore AC=5x$

Now, $\sin \theta +\cos \theta =\frac{BC}{AC}+\frac{AB}{AC}=\frac{4}{5}+\frac{3}{5}=\frac{7}{5}$