Question

solve the foll equation x+y=(2pi)/3,
sin x/sin y =2

Answer 1

\[x + y = \frac{2\pi}{3}\]\[\frac{\sin x}{\sin y}=2\]
\[x = \frac{2\pi}{3} - y\]
\[\frac{\sin(\frac{2\pi}{3}-y)}{\sin y} = 2\]\[\sin(\frac{2\pi}{3})\cos y-\cos(\frac{2\pi}{3})\sin y = 2 \sin y\]\[\frac{\sqrt{3}}{2}\cos y - (-\frac{1}{2})\sin y = 2\sin y\]\[\sqrt{3}\cos y + \sin y = 4 \sin y\]\[\sqrt{3}\cos y = 3\sin y\]\[\frac{\sqrt{3}}{3}=\tan y\]\[y=\tan^{-1}(\frac{\sqrt{3}}{3})\]\[y=\frac \pi 6\]
\[x=\frac{2\pi}{3}-\frac \pi 6\]\[x=\frac \pi 2\]

Answer 2

Nicely done Jyqft