y=4sin（WX+四分之派）cos（WX—四分之派）—2sin（WX—四分之派）cos（WX+四分之派）（W＞0）求化简.谢

Question

y=4sin（WX+四分之派）cos（WX—四分之派）—2sin（WX—四分之派）cos（WX+四分之派）（W＞0）求化简.谢

Answer 1

积化和差公式:
2sinαcosβ=sin(α+β)+sin(α-β)
所以y=4sin(ωx+π/4)cos(ωx-π/4)-2sin(ωx-π/4)cos(ωx+π/4)(ω＞0)
=2[sin(ωx+π/4+ωx-π/4)+sin(ωx+π/4-ωx+π/4)]-[sin(ωx-π/4+ωx+π/4)+sin(ωx-π/4-ωx-π/4)]
=2[sin(2ωx)+sin(π/2)]-[sin(2ωx)+sin(-π/2)]
=2[sin(2ωx)+1]-[sin(2ωx)-1]
=2sin(2ωx)+2-sin(2ωx)+1
=sin(2ωx)+3
如果不懂,请Hi我,祝学习愉快!