Question

If sec θ = $\frac{25}{7}$, then sin θ = ?
(a) $\frac{7}{24}$
(b) $\frac{24}{7}$
(c) $\frac{24}{25}$
(d) None of these

Answer 1

(c) $\frac{24}{25}$
Let us first draw a right $∆$ABC right angled at B and $\angle A=\theta$.
Given: sec θ = $\frac{25}{7}$
But cos θ = $\frac{1}{sec\theta }$= $\frac{AB}{AC}$ = $\frac{7}{25}$
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 = $\frac{BC}{AC}=\frac{24k}{25k}=\frac{24}{25}$