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cos3x=4cos3x−3cosx
sin3x=3sinx−4sin3x
Xét vế trái
vt=cos3x.(4cos3x−3cosx)−sin3x.(3sinx−4sin3x)
=>vt=4(cos6x+sin6x)−3.(sin4x+cos4x)
=>vt=4.(sin2x+cos2x).(sin4x−sin2x.cos2x+cos4x)−3.(sin2x+cos2x)2+6sin2x.cos2x
=>vt=4.[(sin2x+cos2x)2−3sin2x.cos2x]−3+6sin2x.cos2x
=>vt=1−12sin2x.cos2x+6sin2x.cos2x
=>vt=1−3/2.sin2(2x)
=>vt=1−3/4.(1−cos4x)
=>1−3/4.+3/4.cos4x=(2+3can2)/8
=>2+6cos4x=2+3√2
=>6cos4x=3√2
=>cos4x=1√2
=>4x=±π4+k2pi
=>x=±π16+kπ2
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