Question

Biết sin x-cos x=\(\frac{1}{5}\)Tính sin2x

Answer 1

\(sinx-cosx=\frac{1}{5}\Rightarrow\left(sinx-cosx\right)^2=\frac{1}{25}\)

\(\Rightarrow sin^2x+cos^2x-2sinx.cosx=\frac{1}{25}\)

\(\Rightarrow1-sin2x=\frac{1}{25}\)

\(\Rightarrow sin2x=1-\frac{1}{25}=\frac{24}{25}\)

Answer 2

\(sinx-cosx=\frac{1}{5}\)

\(\Leftrightarrow\left(sinx-cosx\right)^2=\frac{1}{25} \)

\(\Leftrightarrow sin^2x+cos^2x-2sinxcosx=\frac{1}{25}\)

\(\Leftrightarrow1-sin2x=\frac{1}{25}\)

\(\Leftrightarrow sin2x=\frac{24}{25}\)