Question : If $\cos\theta=\frac{3}{5}$, then the value of $\sin\theta.\sec\theta.\tan\theta$ is:
Option 1: $\frac{9}{16}$
Option 2: $\frac{16}{9}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{3}$
Correct Answer: $\frac{16}{9}$
Solution :
Given: $\cos\theta=\frac{3}{5}$
We know, $\cos\theta= \frac{\text{Base}}{\text{Hypotenuse}}$
Let, Base = 3, Hypotenuse = 5
So, Perpendicular = $\sqrt{5^2-3^2}=4$
$\sin\theta.\sec\theta.\tan\theta$
= $\frac{\text{Perpendicular}}{\text{Hypotenuse}}×\frac{\text{Hypotenuse}}{\text{Base}}×\frac{\text{Perpendicular}}{\text{Base}}$
= $\frac{4}{5}×\frac{5}{3}×\frac{4}{3}$
= $\frac{16}{9}$
Hence, the correct answer is $\frac{16}{9}$.
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