If `tan^-1 x+tan^-1 y-sin^-1 x=0,` then which of the following are true ?

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true (a) (x+y)/(tan1)=-2 (b) (tan^(-1)x)/(1-tan^(-1)y)=2 (c) (tan^(-1)x)/(1-tan^(-1)y)=2 (d) (x+y)/(cot1)=1

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true (A) (x+y)/(tan1)=-2 (B) (tan^(-1)x)/(1-tan^(-1)y)=2 (C) (x+y)/(tan1)=2 (D) (x+y)/(cot1)=1

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true

If I_(1)=lim_(xto 0)sqrt((tan^(-1)x)/x-(sin^(-1)x)/x) and I_(2)=lim_(xto0)sqrt((sin^(-1)x)/x-(tan^(-1)x)/x) , where |x|lt1 , which of the following statement is true?

If tan^(-1) x + tan^(-1) y - tan^(-1) z = 0 , then prove that : x+ y + xyz = z .

If tan^-1 x + tan^-1y - tan^-1z = 0 , then prove that x + y + xyz = z.

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]

Which of the following is/are true? tan ^(-1)|tan x|=|x|

If tan 3x.tan 3y = 1, then sin(x+y)=?

The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true when the value of xy is "………."