In the triangle $ABC$, angle $BAC=\frac{\pi }{4}$ radians and angle \(ABC=\left( \frac{\pi }{4}+

Question

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]

Accepted Answer

$\frac{AB}{AC}=\sqrt{2}\left( 1-2x+4{{x}^{2}}+... \right)$

2022 TMJC P2 Q4

2022 TMJC P2 Q4

Video Solution:

Solution:

Solution locked