Prove that : `(sin x - sin y)/(cos x + cos y) = tan ((x-y)/2)`

Prove that: (sin x-sin y)/(cos x+cos y)quad =tan(x-y)/(2)

(sin 2x - sin 2y)/(cos 2y-cos 2x) = cot (x+y)

Prove that: (sin x+sin y)/(sin x-sin y)=tan((x+y)/(2))*cot((x-y)/(2))

prove that: (sin2x-sin2y)/(cos2y-cos2x)=cot(x+y)

(dy) / (dx) = (sin x-sin y) (cos x) / (cos y)

Prove the following: (i) ("sin" x+"sin" y)/(cos x+cos y)="tan""(x+y)/(2) (ii) (cos 7x+cos 5x)/("sin" 7x-"sin" 5x)=cot x .

Prove that cos (x + y) = cos x cos y-sin x sin y

Prove that : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos x. sin y)

If sin x + sin y = a, cos x + cos y =b , then tan"" ( x-y )/( 2)="…………."

If sin x + sin y = a and cos x + cos y = b then tan ((x + y) / (2)) is