" 15."(sin x)/(sin3x)

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(sin x)/(sin 3x)

int (sin x) / (sin3x) dx =

(sin x) / (sin2x sin3x) + (sin x) / (sin3x sin4x) + (sin x) / (sin4x sin5x) + .... n

If sin x+sin y=sqrt(3)(cos y-cos x) then (sin3x)/(sin3y)=

lim_ (x rarr0) (tan x-sin x) / (sin3x-3sin x)

(sin x) / (sin3x) + (sin3x) / (cos9x) + (sin9x) / (cos27x) = (tan27x-tan x) / (2)

lim_ (x rarr pi) (sin3x) / (sin2x)

sin7x=sin3x

sin x+sin3x+.......sin(2n-1)x=(sin^(2)nx)/(sin x)

sin x+sin3x+...+sin(2n-1)x=(sin^(2)nx)/(sin x)