把式子根号2sin(派/4-x)+根号6sin(派/4+x)化成Asin(ωx+φ)的形式

把式子根号2sin(派/4-x)+根号6sin(派/4+x)化成Asin(ωx+φ)的形式
把式子根号2sin(派/4-x)+根号6sin(派/4+x)化成Asin(ωx+φ)的形式

把式子根号2sin(派/4-x)+根号6sin(派/4+x)化成Asin(ωx+φ)的形式
原式=√2cos[π/2-(π/4-x)]+√6sin(x+π/4)
=√6sin(x+π/4)+√2cos(x+π/4)
=2√2[√3/2*sin(x+π/4)+1/2cos(x+π/4)]
=2√2[sin(x+π/4)cosπ/6+cos(x+π/4)sinπ/6]
=2√2sin(x+π/4+π/6)
=2√2sin(x+5π/12)