(b)If `(sin (x+y)/sin(x-y))=(a+b)/(a-b)` show that `a tan y=b tan x`.

If (sin(x+y))/(sin(x-y))=(a+b)/(a-b)," then "(tanx)/(tany) is equal to :

int (dx)/(sin (x-a) sin (x-b)) is :

Prove that '(sin (x+y)) / (sin (x-y))=(tan x+tan y)/(tan x- ( tany ))'

If sin y= x sin (a+y) , then (dy)/(dx) is :

If sin(y+z-x),sin(z+x-y),sin(x+y-z) are in A.P ., then tan x , tan y , tan z are in

Show tht tan (x-y)=(tan x-tan y)/(1+tan x tan y)

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 (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 x=sint and y=sinmt show that y=sin(msin^(-1)x)