Question

Solve \(\displaystyle\sqrt{{3}}{\csc{{2}}}{x}={2}\) for all values of x.

Answer 1

\(\displaystyle\sqrt{{3}}{\csc{{\left({2}{x}\right)}}}={2}\)
\(\displaystyle{\csc{{\left({2}{x}\right)}}}=\frac{{2}}{\sqrt{{3}}}=\frac{{2}}{{1.7320508075}}\)
\(\displaystyle{\csc{{\left({2}{x}\right)}}}={1.154700537}\)
\(\displaystyle{\csc{=}}\frac{{1}}{{\sin}},{s}{o}{\sin{{\left({2}{x}\right)}}}=\frac{{1}}{{1.5}}\ldots.={0.866025405}\)
invers \(\displaystyle{\sin{{2}}}{x}={60}\) deg
so x=30 deg