Question

prove that (sin 3A/sinA)+(cos 3A/cos A)=4cos 2A​

Answer 1

Answer:

Step-by-step explanation:

sin3A/sinA+cos3A/cosA

=(sin3AcosA+cos3AsinA)/sinAcosA

=2sin(3A+A)/2sinAcosA [∵, sinαcosβ+cosαsinβ=sin(α+β)]

=2sin4A/sin2A [∵, 2sinαcosα=sin2α]

=(2×2sin2Acos2A)/sin2A

=4cos2A (Proved)