Question

If tan θ = $\frac{4}{3}$, then (sinθ + cosθ) = ?
(a) $\frac{7}{3}$
(b) $\frac{7}{4}$
(c) $\frac{7}{5}$
(d) $\frac{5}{7}$

Answer 1

(c) $\frac{7}{5}$
Let us first draw a right $∆$ABC right angled at B and $\angle A=\theta$.
tan θ = $\frac{4}{3}=\frac{BC}{AB}$
So, AB = 3k and BC = 4k

Using Pythagoras theorem, we get:
AC² = AB² + BC²
⇒ AC² = (3k)² + (4k)²
⇒ AC² = 25k²
⇒ AC= 5k
Thus, sin θ = $\frac{BC}{AC}$ = $\frac{4}{5}$
and cos θ =$\frac{AB}{AC}=\frac{3}{5}$
∴ (sin θ + cos θ) = ( $\frac{4}{5}$ + $\frac{3}{5}$) = $\frac{7}{5}$