高一数学题

化简:sin(π/4-3x)*cos(π/3-3x)-sin(π/4+3x)*sin(π/3-3x)=?
2025-06-22 19:12:36
推荐回答(1个)
回答1:

有如下公式,如果我没记错的话
sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]
cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]
sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]

原式
=1/2*[sin(7π/12-6x)+sin(-π/12)]+1/2*[cos(7π/12)-cos(6x-π/12)]
=1/2sin(7π/12-6x)+1/2cos(7π/12)+1/2cos(7π/12)-1/2sin(7π/12-6x)]
=cos(7π/12)

若化为算式
=cos(60+45)
=cos60cos45-sin60sin45
=(根号下2-根号下6)/4