Question

Giải phương trình sin(x-50◘)=cos(x+120◘)

Answer 1

\(cos\left(x+120^0\right)=sin\left(x-50^0\right)\)

\(\Leftrightarrow cos\left(x+120^0\right)=cos\left(90^0-\left(x-50^0\right)\right)\)

\(\Leftrightarrow cos\left(x+120^0\right)=cos\left(140^0-x\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x+120^0=140^0-x+k360^0\\x+120^0=x-140^0+k360^0\left(vn\right)\end{matrix}\right.\)

\(\Leftrightarrow2x=20^0+k360^0\)

\(\Leftrightarrow x=10^0+k180^0\)