[" If "alpha=2arctan((1+x)/(1-x))" and "beta=arcsin((1-x^(2))/(1+x^(2)))" for "01?]

If alpha=2 tan^(-1)((1+x)/(1-x)) and beta= sin^(-1)((1-x^2)/(1+x^2)) for 0 lt x lt 1 ,then prove that alpha+beta =pi , what the value of alpha+beta will be if x gt 1 .

If quad 2arctan((1+x)/(1-x))in B=arcsin((1-x^(2))/(1+x^(2))) for 0

int(x^(2)arctan x)/(1+x^(2))dx

If alpha=tan^(-1)((4x-4x^(3))/(1-6x^(2)+x^(2))),beta=2sin^(-1)((2x)/(1+x^(2))) and (tan pi)/(8)=k, then (a) alpha+beta=pi for x in[(1,1)/(k)]( b) alpha+beta for x in(-k,k)(c)alpha+beta=pi for x in[(1,1)/(k)](d)alpha+beta=0 for x in[-k,k]

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [(1,1)/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [(1,1)/k] (d) alpha+beta=0 for x in [-k , k]

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^2)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [(1,1)/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [(1,1)/k] (d) alpha+beta=0 for x in [-k , k]

If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)),beta=2sin^(-1)((2x)/(1+x^2)) and tanpi/8=k , then (a) alpha+beta=pi for x in [1,1/k] (b) alpha+beta for x in (-k , k) (c) alpha+beta=pi for x in [1,1/k] (d) alpha+beta=0 for x in [-k , k]

If tan alpha=(x)/(x+1) and tan beta=(1)/(2x+1), then alpha+beta is

tan alpha=(1+2^(-x))^(-1),tan beta=(1+2^(x+1))^(-1)alpha+beta

If tan alpha=(1+2^(-x))^(-1), tan beta=(1+2^(x+1))^(-1) then alpha+beta equals