If Pcos α = 3 and 4tan α = Q, then what is the relation between P and Q, which is independent of α ?

Correct option is C

Given:

Pcos α = 3

4tan α = Q

Formula Used:

We use the following trigonometric identities:

sin²α + cos²α = 1

tan α = sin α / cos α

Solution:

$$P \cos \alpha = 3 \\\implies \cos \alpha = \frac{3}{P} \\\implies \sec \alpha = \frac{P}{3} \\4 \tan \alpha = Q \\\implies \tan \alpha = \frac{Q}{4} \\\text{From the given concept, we get} \\\sec^2 \alpha - \tan^2 \alpha = 1 \\\implies \frac{P^2}{9} - \frac{Q^2}{16} = 1$$​​​