If Sin θ = 3/5, then find the value of tan 2θ

Correct option is C

Given:
sin θ = 3/5
This forms a right triangle where:
Opposite side = 3
Hypotenuse = 5
Formula:
​$$\tan 2\theta = \frac{2 \tan \theta}{1 - \tan^2 \theta}$$​​

Solution:

Use Pythagoras to find adjacent side:
adjacent = √(5² − 3²) = √(25 − 9) = √16 = 4

So, cos θ = 4/5, and tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4

tan θ = 3/4

Now,
tan 2θ $$= \frac{2 \cdot \frac{3}{4}}{1 - \left(\frac{3}{4}\right)^2} = \frac{3/2}{7/16} = \frac{48}{14} = \frac{24}{7}$$​​

Final Answer:
(C) 24/7