x sin y+y sin x=0

Prove that : sin x sin y sin (x - y) + sin y sin z sin (y- z)+ sin z sin x sin (z - x) + sin (x - y) sin (y-z)sin (z- x) = 0 .

(sin x + sin y) / (sin x-sin y) = tan ((x + y) / (2)) * cot ((xy) / (2))

What ( sin x cos y + cos x sin y) (sin x cos y - cos x sin y) equal to ?

If sin x + sin y + sin z = 0 and cos x + cos y + cos z = 0 then prove that cot (x+y)/2 = cot z and cos (x-y)/2 = pm 1/2

If x sin y+y cos x=pi , then the value of y''(0) is -

Show that sin (x-y) + sin (y-z) + sin (z-x) + 4sin((x-y)/(2)) sin( (y-z)/(2)) sin((z-x)/(2)) =0

Show that sin (x-y) + sin (y-z) + sin (z-x) + 4sin((x-y)/(2)) sin( (y-z)/(2)) sin((z-x)/(2)) =0

If cos(x - y)= -1 , show that cos x + cos y = 0 and sin x + sin y = 0 .

If sin ((x+y)/( 2)) =sinx +sin y and sin ((x-y)/( 2 ))ne 0,then (dy)/(dx)=