`lim_(x->0)(sin(tanx)-tan(sinx))/(tan^(- 1)(sin^(- 1)x)-sin^(- 1)(tan^(- 1)x))=`

tan(sin^(-1)x)

lim_ (x rarr0) (sin (tan x) -tan (sin x)) / (tan ^ (- 1) (sin ^ (- 1) x) -sin ^ (- 1) (tan ^ (- 1) x )) =

lim_ (x rarr0) (sin x-tan x) / (tan ^ (- 1) x-sin ^ (- 1) x) =

sin^(-1)((1-tan^(2)x)/(1+tan^(2)x))

The value of lim_(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7+(sin^(- 1)x)^6+3sin^5x) equal to :

The value of lim_(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7+(sin^(- 1)x)^6+3sin^5x) equal to :

lim_(x rarr 0) (tan (sin^(-1) 3x))/(sin^(-1) (2 tan x)) =

lim_(x rarr0)(sin^(-1)x+3x)/(tan x+2sin((1)/(2)sin^(-1)x)[3-4sin^(2)((1)/(2)sin^(-1)x)])=

lim_(x rarr0)(sin^(-1)x-tan^(-1)x)/(x^(2))