Question

Sin x - sin y /cos x + cos y =tan x-y / 2

Answer 1

sin

x

−

sin

y

=

2

cos

x

+

y

2

sin

x

−

y

2

a

n

d

cos

x

+

cos

y

=

2

cos

x

+

y

2

cos

x

−

y

2

Answer 2

Answer:

by using the formula

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

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

sin x - sin y / cosx + cos y

= 2 {cos(x+y)/2} {sin (x-y)/2} / 2{cos(x+y)/2} {cos(x-y)/2}

= { sin(x-y)/2} / {cos (x-y)/2} = tan(x-y)/2.