“y=2sinx-3cosx取最大值时tanx的值是”,怎么做?

y=2sinx-3cosx
=13^0.5(sinx*cosa-cosx*sina) sina=3/13^0.5,cosa=2/13^0.5
=13^0.5sin(x-a)
x=TT/2+a时最大
tanx=tan(TT/2+a)
=-ctga=-cosa/sina=-2/3