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

tan $\theta$ = $\frac{4}{3}$

$tanA=\frac{Perpendicularside}{Baseside}=\frac{4}{3}$

Perpendicular = 4 & Base = 3

$(Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$ (using Pythagoras theorem.)

therefore,Hypotenuse = 5

$sin\theta =\frac{Perpendicularside}{Hypotenuse}=\frac{4}{5}$

$cos\theta =\frac{Baseside}{Hypotenuse}=\frac{3}{5}$

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