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 $b-c\approx \frac{2ax}{\sqrt{3}}$.
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