Question

Cho sinx + cosx = \(\sqrt{2}\). Tìm x.

Answer 1

\(sinx+cosx=\sqrt{2}\) \(\Leftrightarrow\) \(x\left(sin+cos\right)=\sqrt{2}\)

\(\Leftrightarrow\) \(x=\dfrac{\sqrt{2}}{\left(sin+cos\right)}\)

Answer 2

\(sinx+cosx=\sqrt{2}\Leftrightarrow\left(sin^2x+cos^2x+2sinx.cosx\right)=2\)

\(\Leftrightarrow1+2sinx.cosx=2\Leftrightarrow sinx.cosx=\dfrac{1}{2}\Leftrightarrow sin^2x=\dfrac{1}{2}\Leftrightarrow sinx=\dfrac{\sqrt{2}}{2}\)

Giải trên máy tính =>x=45.