cos(A-B)+cos(A+B+π/2)求详细解答过程

cos(A-B)+cos(A+B+π/2)
=cos(A-B)+cos(A+B)cosπ/2-sin(A+B)sinπ/2
=cos(A-B)-sin(A+B)
=cosAcosB+sinAsinB-sinAcosB-sinBcosA
=cosA(cosB-sinB)+sinA(sinB-cosB)
=(cosB-sinB)(cosA-sinA)
=√2(cosπ/4cosB-sinπ/4sinB)·√2(cosπ/4cosA-sinπ/4sinA)
=2cos(π/4+B)cos(π/4+A)
如果不知道A、B角度,已经不能再化简了