Q.30quad y=sin sin sin x

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

Prove that : sin (y + z-x) + sin (z + x-y) + sin (x +y-z)-sin (x+y+z) = 4 sin x sin y sin z .

if y = sin x ^ (sin x ^ (sin x))

Find the value of x in the following equation sin 2x = sin 60° cos 30° - cos 60° sin 30°

The value of sinx siny sin(x-y)+sinysinz sin(y-z) +sinz sinx sin(z-x)+sin(x-y)sin(y-z)sin(z-x), is

If y=sin x*sin2x.sin3x......sin nx, find y'

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

If y=(sin x) ^(sin x ^sin x ....oo) then prove that dy/dx=(y^2 cot x)/(1-y log (sin x))

If y=(sin x) ^(sin x ^sin x ....oo) then prove that dy/dx=(y^2 cot x)/(1-y log (sin x))