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

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

" 1.If sin x+sin y=(1)/(4),cos x+cos y=(1)/(3) then tan((x+y)/(2))=

Show that (i) cos x+cos y=2 cos (x+y)/(2) cos (x-y)/(2) (ii) cos x-cos y=-2 sin (x+y)/(2) sin (x-y)/(2) (iii) sin x+sin y=2 sin (dot(x)+y)/(2) cos (x-y)/(2) (iv) sin x-sin y=2 cos (x+y)/(2) sin (x-y)/(2)

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

Prove that (i) 2 cos x cos y=cos (x+y)+cos (x-y) (ii) -2 . sin x sin y=cos (x+y)-cos (x-y) (iii) 2 sin x cos y=sin (x+y)+sin (x-y) (iv) 2 cos x sin y=sin (x+y)-sin (x-y)

If cot theta = cos (x+y) "and" cot phi = cos (x-y), "show that" tan (theta- phi)=(2sin x sin y )/(cos^(2) x + cos^(2) y)

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

If y = Tan ^(-1) ((cos x- sin x)/(cos x + sin x)) then (d ^(2) y)/(dx ^(2))=

The value of (sin x cos y + cos x sin y)^2+(cos x cos y -sin x sin y)^2 is equal to

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