2022 ACJC J2 MYE Q1
In the triangle $ABC$, $AB=2$, angle $ABC=\theta $ radians and angle $BAC=\frac{\pi }{4}$ radians.
(i)
Show that $BC=\frac{2}{\sin \theta +\cos \theta }$.
[3]
(ii)
Given that $\theta $ is a sufficiently small angle, show that $BC\approx p+q\theta +r{{\theta }^{2}}$, for constants $p$,$q$ and $r$ to de determined.
[3]
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