​$$\text{If } \cot \theta = \frac{3}{4}, \text{ then find the value of } \sin 3\theta.$$​​

Correct option is A

Given:

$$\cot\theta=\frac{3}{4}$$​​

Find $$\sin 3\theta$$​​

Formula Used:

​$$\sin 3\theta=3\sin\theta-4\sin^{3}\theta$$​​

Solution:

From $$\cot\theta=\frac{3}{4},$$​take a right triangle with base = 3, perpendicular = 4, hypotenuse = 5.
So, $$\sin\theta=\dfrac{4}{5}.$$​​

$$\sin 3\theta \\ \ \\=3\left(\frac{4}{5}\right)-4\left(\frac{4}{5}\right)^3 \\ \ \\=\frac{12}{5}-\frac{256}{125}\\ \ \\=\frac{300-256}{125}\\ \ \\=\frac{44}{125}$$​​