Show that the expression `(tan(x+alpha))/(tan(x-alpha))` cannot lie between the values `tan^2 (pi/4-alpha)` and `tan^2(pi/4+alpha)`

int(tan x-tan alpha)/(tan x+tan alpha)dx

Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi/4, 3pi/4 cannot lies between (1- sin2 alpha)/(1+ sin 2alpha) and (1+ sin2 alpha)/(1- sin 2alpha) .

If tan alpha= sqrt2-1 then the value of tan alpha-cot alpha = ?

If tan alpha = sqrt3+2 , then the value of tan alpha - cot alpha is

If 0 lt alpha lt (pi)/(16) and (1+tan alpha)(1+tan4alpha)=2 , then the value of alpha is equal to

If alpha in (-(pi)/(2), 0) , then find the value of tan^(-1) (cot alpha) - cot^(-1) (tan alpha)

If (sin(theta+alpha))/(cos(theta-alpha))=(1-m)/(1+m), prove that tan((pi)/(4)-theta)tan((pi)/(4)-alpha)=m

If n is an integer,prove that tan(n pi+alpha)=tan alpha