Sina^4+2√3sinacosa-cos^4化简
问题描述：
Sina^4+2√3sinacosa-cos^4
化简
答
原式=[(1-cos2a)/2]²+√3sin2a-[(1+cos2a)/2]²
=-cos2a+√3sin2a
=2(√3sin2a/2-cos2a/2)
=2(cosπ/6*sin2a-sinπ/6*cos2a)
=2sin(2a-π/6)
答
Sina^4+2√3sinacosa-cosa^4
=√3sin2a+(sina^2+cos^2)(sina^2-cosa^2)
=√3sin2a+sina^2-cosa^2
=√3sin2a-(cosa^2-sina^2)
=2(√3/2sin2a-1/2cos2a)
=2(sin2acosπ/6-cos2asinπ/6)
=2sin(2a-π/6)