In triangle $PQR$, angle $PQR=\frac{\pi }{4}$ radians and angle \(PRQ=\frac{\pi }{4}+\frac{x}{2}

Question

In triangle $PQR$, angle $PQR=\frac{\pi }{4}$ radians and angle $PRQ=\frac{\pi }{4}+\frac{x}{2}$ radians. Given that $x$ is sufficiently small for ${{x}^{5}}$ and above to be ignored, show that $\frac{PR}{QR}\approx \frac{\sqrt{2}}{2}\left( 1+\frac{{{x}^{2}}}{8}+\frac{5{{x}^{4}}}{384} \right)$.[7]

Accepted Answer

$\displaystyle \frac{PR}{QR}\approx\frac{\sqrt2}{2}\left(1+\frac{x^2}{8}+\frac{5x^4}{384}\right)$.

2013 PJC P1 Q4

2013 PJC P1 Q4

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