sin(A-3/4π)cos(A-π/4)
=sin(A-3/4π)sin(π/2-(A-π/4))
=sin(A-3/4π)sin(-A+3/4π)
=-sin(A-3/4π)sin(A-3/4π)
=-1/4
即sin^2(A-3/4π)=1/4
根据二倍角公式
cos2A=1-2sin^2A
求出cos2A
再次二倍角公式,进而求出cos4A
以下略去.
sin(A-3/4π)cos(A-π/4)
=sin(A-3/4π)sin(π/2-(A-π/4))
=sin(A-3/4π)sin(-A+3/4π)
=-sin(A-3/4π)sin(A-3/4π)
=-1/4
即sin^2(A-3/4π)=1/4
根据二倍角公式
cos2A=1-2sin^2A
求出cos2A
再次二倍角公式,进而求出cos4A
以下略去.