Are `x^(2)-1` and `tan x=(sinx)/(cos x)` rational expressions ?

Integrate (sinx)/(1+cos^(2)x) w.r.t.x ,

x sinx(dy)/(dx)+(x cos x+sinx)y=sinx

simplify : tan^(-1) ""((a cos x- b sin x )/(b cos x + a sin x ) ) (- pi )/(2) lt x lt pi/2 , a/b tan x gt -1

Find the derivative with tan^(-1) ((sinx )/(1 + cos x)) with respect to tan^(-1) ((cos x)/(1 + sin x))

Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x), b in R . Equation has solutions if

Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x), b in R . Equation has solutions if

(1 + cos 4 x )/( cot x - tan x )