If cos A = $\dfrac{4}{5}$, then the value of tan A is

1. $\dfrac{3}{5}$

2. $\dfrac{3}{4}$

3. $\dfrac{4}{3}$

4. $\dfrac{5}{3}$

Let ABC be a right angle triangle with ∠B = 90°.

By formula,

cos A = $\dfrac{\text{Base}}{\text{Hypotenuse}}$

Substituting values we get :

$\Rightarrow \dfrac{4}{5} = \dfrac{AB}{AC}$

Let AB = 4x and AC = 5x.

In right angle triangle ABC,

⇒ AC² = AB² + BC²

⇒ (5x)² = (4x)² + BC²

⇒ 25x² = 16x² + BC²

⇒ BC² = 25x² - 16x²

⇒ BC² = 9x²

⇒ BC = $\sqrt{9x^2}$ = 3x.

By formula,

tan A = $\dfrac{\text{Perpendicular}}{\text{Base}}$

= $\dfrac{BC}{AB} = \dfrac{3x}{4x} = \dfrac{3}{4}$.

Hence, Option 2 is the correct option.