Question

若2sinθ+3cosθ=0,求2cos2θ+3sin2θ的值

Answer 1

2sinθ+3cosθ=0

2sinθ=-3cosθ

sinθ/cosθ=-3/2

tanθ=-3/2

2cos2θ+3sin2θ

=2*[1-(tanθ)^2]/[1+(tanθ)^2]+3*2(tanθ)/[1+(tanθ)^2]

=2*(1-9/4)/(1+9/4)+6*(-3/2)/(1+9/4)

=(-5/2)/(13/4)+(-9)/(13/4)

=(-5/2-9)/(13/4)

=(-23/2)/(13/4)

=-23/2*4/13

=-46/13