Question

Solve:

\[ \int \frac{\sin x}{\sin (x+a)} \, dx. \]

Hint:

Use trigonometric identities to simplify integrals involving sine and cosine.

Answer 1

We use the substitution: \[ I = \int \frac{\sin x}{\sin (x+a)} dx. \] Using the identity: \[ \sin (x+a) = \sin x \cos a + \cos x \sin a, \] we express the integral in a solvable form and integrate accordingly.