 Hello and welcome to the session, I am Asha and I am going to help you with the following question which says, prove that sin x minus sin y upon cos x plus cos y is equal to tan x minus y upon 2. Let us begin with the solution and we will try to solve the left hand side which is sin x minus sin y upon cos x plus cos y and show that it is equal to the right hand side. Now sin x minus sin y is equal to 2 cos x plus y upon 2 into sin x minus y upon 2 and the formula of cos x plus cos y is 2 cos x plus y upon 2 into cos x minus y upon 2. Now in cancelling the common factors of the numerator and denominator 2 with 2 and cos x plus y upon 2 with cos x plus y upon 2 we have sin x minus y upon 2 upon cos x minus y upon 2 which is further equal to tan x minus y upon 2 since sin theta upon cos theta is equal to tan theta and first we have tan x minus y upon 2 which is equal to the right hand side and hence we can say that l it is equal to the r it is or sin x minus sin y upon cos x plus cos y is equal to tan x minus y upon 2 hence proved. So this completes the solution take care and have a good day.