Question : If $\sin \theta=\frac{6}{10}$ and $\cos\theta = \frac{8}{10}$, then $\sin2\theta =$ ______.
Option 1: $\frac{10}{8}$
Option 2: $\frac{12}{10}$
Option 3: $\frac{16}{10}$
Option 4: $\frac{24}{25}$
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Correct Answer: $\frac{24}{25}$
Solution :
Given, $\sin \theta=\frac{6}{10}$ and $\cos\theta = \frac{8}{10}$
$\sin2\theta =2\sin\theta\cos\theta$
⇒ $\sin2\theta = 2\times \frac{6}{10}\times\frac{8}{10}$
⇒ $\sin\theta = 2\times \frac{3}{5}\times \frac{4}{5}$
⇒ $\sin2\theta = \frac{24}{25}$
Hence, the correct answer is $\frac{24}{25}$.
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