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

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

Show 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)

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

Prove that |(1,x,y),(0, sin x, sin y),(0, cos x,cos y)|= sin (x-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 : (sin (x+y))/(sin (x-y) )= (sin x. cos y + cos x . Sin y)/(sin x. cos y-cos 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 and cos x + cos y = b then tan ((x + y) / (2)) is

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