sin(a+b)cosa-1/2[sin(2a+b)-sinb]化简
1个回答

sin(a+b)cosa-1/2[sin(2a+b)-sinb]

=(sinacosb+cosasinb)cosa-1/2(sin2acosb+cos2asinb-sinb)

和差公式,全部打开

=sinacosacosb+cos²asinb-1/2(2sinacosacosb+(2cos²a-1)sinb-sinb)

二倍角公式打开

=sinacosacosb+cos²asinb-1/2(2sinacosacosb+2cos²asinb-sinb-sinb)

依次化简

=sinacosacosb+cos²asinb-sinacosacosb+cos²asinb-sinb

=-sin