Question

prove that sin7x+sin5x+sin9xsin3x/cos7x+cos5x+cos9x+cos3x=tan6x​

Answer 1

Answer:

LHS = [(sin7x + sin5x) + (sin9x + sin3x)]/[(cos7x + cos5x) + (cos9x + cos3x)]

use the formula,

sinC + sinD = 2sin(C+D)/2.cos(C-D)/2

cosC + cosD = 2cos(C+D)/2.cos(C-D)/2

= {2sin6x.cosx +2sin6x.cos3x}/{2cos6x.cosx + 2cos6x.cos3x}

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

= sin6x/cos6x

= tan6x = RHS