\(cos\left(x+y\right)=cosx.cosy-sinx.siny\)
Đặt y=2x
=> \(cos\left(x+2x\right)=cosx.cos2x-sĩn.sin2x\)
\(\Leftrightarrow cos3x=cosx.\left(2.cos^2x-1\right)-sinx.2sinx.cosx\)
\(\Leftrightarrow cos3x=cosx\left(2cos^2x-1-2sin^2x\right)\)
\(\Leftrightarrow cos3x=cosx\left(2cos^2x-1-2\left(1-cos^2x\right)\right)\)
\(\Leftrightarrow cos3x=cosx\left(4cos^2x-3\right)\)
\(\Leftrightarrow cos3x=4\left(cosx\right)^3-3cosx\)
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