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int(sin 2x)/(sin x)dx

sin2xsinxdx \int \frac{\sin 2 x}{\sin x} d x =

Full solution

Q. sin2xsinxdx \int \frac{\sin 2 x}{\sin x} d x =
  1. Simplify using trigonometric identities: Simplify the integral using trigonometric identities.\newlinesin2xsinxdx=2sinxcosxsinxdx=2cosxdx \int \frac{\sin 2x}{\sin x} \, dx = \int \frac{2 \sin x \cos x}{\sin x} \, dx = \int 2 \cos x \, dx
  2. Integrate 22 cos x: Integrate 2cosx2 \cos x.\newline2cosxdx=2sinx+C \int 2 \cos x \, dx = 2 \sin x + C