`sin x*sin y=-(1)/(2)[cos(x+y)-cos(x-y)]`

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

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

If sin x + sin y = 1/2 and cos x + cos y = 1 then tan (x + y)

Simplify by reducing to a single term : sin (x -y) cos x - cos (x-y) sin x.

If 3sin(x y)+4cos(x y)=5 , then (dy)/(dx)= (a) y/x (b) (3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y)) (c) (3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y)) (d) none

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

If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= ___________ (a) 2sin3x (b) 0 (c) 1 (d) none of these

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

Prove that : (cos x - cos y)^(2) + (sin x - sin y)^(2) = 4 sin^(2) ((x - y)/(2))