x sin y + y sin x = 0

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

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 .

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

If cos x + cos y + cos alpha = 0 and sin x + sin y + sin alpha = 0 then cot ((x + y) / (2)) =

If cos x + cos y + cos alpha = 0 and sin x + sin y + sin alpha = 0 , then cot((x+y)/(2)) =

cos x + cos y + cos alpha = 0 and sin x + sin y + sin alpha = 0 then cot ((x + y) / (2)) is

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

The solution of (dy) / (dx) + (y cos x + sin y + y) / (sin x + x cos y + x) = 0 is

If x sin (a + y) + sin a cos (a + y)= 0 , then prove that (dy)/(dx)= (sin^(2) (a + y))/(sin a)