2022 TMJC P2 Q4
In the triangle $ABC$, angle $BAC=\frac{\pi }{4}$ radians and angle $ABC=\left( \frac{\pi }{4}+2x \right)$ radians. Show that $\frac{AB}{AC}=\frac{\sqrt{2}\cos 2x}{\cos 2x+\sin 2x}$.
[3]
Given that $x$ is sufficiently small for which ${{x}^{3}}$ and higher powers of $x$ can be ignored, find the series expansion of $\frac{AB}{AC}$ in ascending powers of $x$.
[4]
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