(¥E303 + X6W09) 4 (15800 + £/ 900) |,X9 U= g e + X6, U1%) + (Y5 Wis

1.	(¥E303 + X6W09) 4 (15800 + £/ 900) \|,X9 U= g e + X6, U1%) + (Y5 Wis 7 ¥/ ugs)
Answer» LHS = [(sin7x + sin5x) + (sin9x + sin3x)]/[(cos7x + cos5x) + (cos9x + cos3x)] use the formula, sinC + sinD = 2sin(C+D)/2.cos(C-D)/2cosC + 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

(¥E303 + X6W09) 4 (15800 + £/ 900) |,X9 U= g e + X6, U1%) + (Y5 Wis 7 ¥/ ugs)

Answer»

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

use the formula, sinC + sinD = 2sin(C+D)/2.cos(C-D)/2cosC + 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