1.

The value of (sin 7x + sin 5x) /(cos 7x + cos 5x) + (sin 9x + sin 3x) / (cos 9x + cos 3x) is

Answer»

Answer:

LHS = [(sin7x + SIN5X) + (sin9x + sin3x)] [(COS7X + cos5x) + (cos9x + cos3x)]

use the FORMULA,

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

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

- 2sin(x(cosx + cos3x)/ 2cos6x(cosx+cos3x)

= sin6x/cos6x

= tan6x = RHS

hence proved

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