Prove the following Identities
`(sin(x+y)-2sinx+sin(x-y))/(cos(x+y)-2cosx+cos(x-y))=tanx`

(sin 2x - sin 2y)/(cos 2y-cos 2x) = cot (x+y)

Prove that: (sin5x-2sin3x+sinx)/(cos5x-cos x)=tanx

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

What is the value of {sin (x+y) -2 sin x+ sin(x-y)} /[cos (x-y) +cos (x+ y)-2 cos x] xx [(sin 10x- sin 8x)/ (cos-10x + cos 8x)] ? {[sin (x+y] -2 sin x+ sin(x-y)}//[cos (x-y) +cos (x+ y)-2 cos x]} xx [(sin 10x-sin 8x)//(cos10x + cos 8x)] का मान क्या है?

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-sin y)/(cos x+cos y)quad =tan(x-y)/(2)

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 y= (sinx -cos x )^((sin x +cos x ) ),then (dy)/(dx)=