√2sin(x-π/4)+√6cos(x-π/4)
=2√2[(1/2)sin(x-π/4)+(√3/2)cos(x-π/4)]【提√(a²+b²)】
=2√2[sin(x-π/4)cos(π/3)+cos(x-π/4)sin(π/3)]
=2√2sin(x-π/4+π/3)
=2√2sin(x+π/12)
【如果熟悉辅助角公式更简单:asinα+bcosα=√(a²+b²)sin(α+φ),其中tanφ=b/a】
√2sin(x-π/4)+√6cos(x-π/4)
=2√2[(1/2)sin(x-π/4)+(√3/2)cos(x-π/4)]【提√(a²+b²)】
=2√2[sin(x-π/4)cos(π/3)+cos(x-π/4)sin(π/3)]
=2√2sin(x-π/4+π/3)
=2√2sin(x+π/12)
【如果熟悉辅助角公式更简单:asinα+bcosα=√(a²+b²)sin(α+φ),其中tanφ=b/a】