Question

Se cossec x=2, calcule cos 2x.

Answer 1

$\displaystyle \csc{x}=2~\Leftrightarrow~\frac{1}{\sin{x}}=2~\Leftrightarrow~\sin{x}=\frac{1}{2}~\Rightarrow~\sin^2{x}=\frac{1}{4}\\\\\cos{2x}=\cos^2{x}-\sin^2{x}=1-2\sin^2{x}=\frac{1}{2}$