√2sin(x-π／4）+√6cos（x-π／4）化简

√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】

答：
√2sin(x-π/4)+√6cos(x-π/4)
=2√2*[(1/2)sin(x-π/4)+(√3/2)cos(x-π/4)]
=2√2*sin(x-π/4+π/3)
=2√2*sin(x+π/12)

√2sin(x-π／4）+√6cos（x-π／4）
=2√2[(1/2)sin(x-π／4）+(√3/2)cos（x-π／4）]
=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)