Correct answer is (c) 24/25
Let us first draw a right ∆ABC right angled at B and ∠A = θ.
Given sec θ = 25/7
But cos θ = 1/secθ = AB/AC = 7/25
Thus, AC = 25k and AB = 7k
Using Pythagoras theorem, we get:
AC2 = AB2 + BC2
⇒ BC2 = AC2 − AB2
⇒ BC2 = (25k)2 − (7k)2
⇒ BC2 = 576k2
⇒ BC = 24k
∴ sin θ = BC/AC = 24k/25k = 24/25
