If P cos α = 3 and 4 tan α = Q, then what is the relation…

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

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. $\frac{P^2}{9}-\frac{Q^2}{16}=1$ .

We know that,

⇒ sec²θ - tan²θ = 1

Now,

⇒ P cos α = 3

⇒ cos α = 3/P

⇒ sec α = P/3

⇒ 4 tan α = Q

⇒ tan α = Q/4

From the given concept, we get

⇒ sec² $\alpha$ - tan² $\alpha$ = 1

⇒ $\frac{P^2}{9}-\frac{Q^2}{16}=1$

SSC CGL 2023 PYQ — Question 64