Answer
See proof below.
Work Step by Step
Step 1. Draw a diagram as shown in the figure. the know quantities are the three angles A, B, C and side $a$.
Step 2. The height of the triangle $h=a\cdot cosB$
Step 3. Use the Law of Sines as $\frac{AB}{sinC}=\frac{a}{sinA}$, we get the base $AB=a\frac{sinC}{sinA}$
Step 4. The area of the triangle =$\frac{1}{2}AB\times h=\frac{1}{2}a\frac{sinC}{sinA}\times a\cdot cosB
=\frac{a^2sinBsinC}{2sinA}$
