tan(2x)/(3)=sqrt(3)

tan x*tan(x+(pi)/(3))*tan(x+(2 pi)/(3))=sqrt(3)

If f(x)=tan^(-1)((sqrt(3)x-3x)/(3sqrt(3)+x^(2)))+tan^(-1)(x/(sqrt(3))),0lexle3, then range of f(x) is

If f(x)=tan^(-1)((sqrt(3)x-3x)/(3sqrt(3)+x^(2)))+tan^(-1)(x/(sqrt(3))),0lexle3, then range of f(x) is

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

tan^(2)x-(1+sqrt(3))tan x+sqrt(3)<0

If tan theta=(2x-K)/(K sqrt(3)) and tan varphi=(x sqrt(3))/(2K-x), then show that | varphi-theta|=30^(@)

int(dx)/(4sin^(2)x+3cos^(2)x) is equal to a) (sqrt(3))/(4)tan^(-1)""((2tanx)/(sqrt(3)))+C b) (1)/(2sqrt(3))tan^(-1)""((tanx)/(sqrt(3)))+C c) (2)/(sqrt(3))tan^(-1)""((2tanx)/(sqrt(3)))+C d) (1)/(2sqrt(3))tan^(-1)""((2tanx)/(sqrt(3)))+C

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

tan^(2)x -(1+sqrt(3))tanx + sqrt(3)=0