Question

Find the value of $\sin 2a$ when $\cos a=\frac{3}{5}$

• A. $\frac{24}{25}$
• B. $\frac{12}{25}$
• C. $\frac{24}{5}$
• D. None of these

Answer 1

Answer: (A)

$\frac{24}{25}$

Given $\cos a=\frac{3}{5}$

To find $\sin 2a$

${\sin }^{2}a+{\cos }^{2}a=1$

${\sin }^{2}a=1-\frac{3^2}{5^2}$

${\sin }^{2}a=\frac{25-9}{5^2}=\frac{16}{5^2}$

$\Rightarrow {\sin }^{2}a=\frac{4^2}{5^2}\Rightarrow \sin a=\frac{4}{5}$

$\sin 2a=2\sin a\cos a$

$\sin 2a=2\times \frac{4}{5}\times \frac{3}{5}\Rightarrow \frac{24}{25}$