sin (4)/(5) cos (3)/(5)+cos (4)/(5) sin (3)/(5)

To solve the expression \( \sin \frac{4}{5} \cos \frac{3}{5} + \cos \frac{4}{5} \sin \frac{3}{5} \), we can use the angle addition formula for sine:<br /><br />\[ \sin(A + B) = \sin A \cos B + \cos A \sin B \]<br /><br />In this case, we have \( A = \frac{4}{5} \) and \( B = \frac{3}{5} \). So, the expression becomes:<br /><br />\[ \sin \left( \frac{4}{5} + \frac{3}{5} \right) \]<br /><br />Now, we can simplify the angle inside the sine function:<br /><br />\[ \frac{4}{5} + \frac{3}{5} = \frac{7}{5} \]<br /><br />So, the expression becomes:<br /><br />\[ \sin \left( \frac{7}{5} \right) \]<br /><br />Therefore, the correct answer is \( \sin \left( \frac{7}{5} \right) \).