Question

Prove that (sin7x+sin5x)+(sin9x+sin3x)/(cos7x+cos5x)+(cos9x+cos3x)=tan6x

Answer 1

Answer:

Step-by-step explanation:

(sin7x+sin5x)+(sin9x+sin3x)/(cos7x+cos5x)+(cos9x+cos3x)

Using SinA + SinB = 2Sin(A+B/2)Cos(A-B/2)

          CosA + CosB = 2Cos(A+B/2)Cos(A-B/2)

= 2sin(7x+5x/2)cos(7x-5x/2)+ 2sin(9x+3x/2)cos(9x-3x/2) / 2cos(7x+5x/2)cos(7x-5x/2) + 2cos(9x+3x/2)cos(9x-3x/2)

= 2sin6xcosx+2sin6xcos3x/ 2cos6xcosx+2cos6xcos3x

= 2sin6x (cosx + cos3x) / 2cos6x(cosx+cos3x)

= sin6x/cos6x

= tan6x

= R.H.S

Hence proved.

Answer 2

Here we use the identities , Sinx+siny and cosx+cosy...