If secθ = 13/5, then what is the value of 2sinθ-3cosθ / 4sinθ-9cosθ ?

Question

If \(\sec \theta = \frac{13}5, \) then what is the value of \(\frac{2\sin \theta - 3\cos \theta}{4\sin \theta - 9cos \theta}\)?

(a) 1

(b) 2

(c) 3

(d) 4

Answer 1

Correct option is (c) 3

\(\sec \theta = \frac{13}5\)

\(\sec \theta = \frac HB = \frac{13}5\)

Using Pythagoras Theorem,

H² = P² + B²

13² = P² + 5²

P² = 144

P = 12

Now,