Maclaurin Series Q1

Maclaurin Series - Small Angle Approximation Q1

In the triangle \(ABC\), angle \(BAC=\frac{\pi }{3}\) radians, angle \(ABC=\left( \frac{\pi }{3}+x \right)\) radians and angle \(ACB=\left( \frac{\pi }{3}-x \right)\) radians, where \(x\) is small. The lengths of \(BC\), \(AC\) and \(AB\) are denoted by \(a\), \(b\) and \(c\) respectively.

By using the sine formula, or otherwise, show that \(b-c\approx \frac{2ax}{\sqrt{3}}\).