SSC CHSL 7-Jan-2017 Shift 1 Paper

We know that, cos (x+y) = cosx cosy - sinx siny ----(i)
and cos (x-y) = cosx cosy + sinx siny -----(ii)
Subtracting equations (ii) from (i), we get :
cos (x+y) - cos (x-y) = - 2 sinx siny ----------(iii)
Let x+y = C and x-y = D
⇒ x=

C+D

2

⇒ and y=

C−D

2

Substituting above values in equation (iii)
⇒ cosC−cosD =−2sin(

C+D

2

)sin(

C−D

2

)
⇒ cosC−cosD =2sin(

C+D

2

)sin(

D−C

2

)