Prove the inequality
arc `tan x_(2) -arc tan x_(1) lt x_(2) -x_(1)` where `x_(2) gt x_(1)`

Solve the following inequalities tan^(2) (arc sin x)gt 1

Solve the inequality (tan^(-1)x)^(2)-4tan^(-1)x+3>0 for x.

int x^(3) "arc" tan x dx .

Prove the inequalities x-x^(2) lt In (1+x) "at" x gt 0

The inequality x^(2)-3x gt tan^(-1) x is ture in

Solve the following inequalities arc sin x gt arc cos x

Solve the following inequality: arc cot^(2)x-5 arc cotx+6gt0

Prove the inequalities tan x gt x + x^(3) //3 " at" 0 lt x lt pi//2

Compute the integrals : int_(0)^(1) x "arc tan x dx

Statement-1 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) gt x_(2) when 0 lt a lt 1 . and Statement-2 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) lt x_(2) when a gt 1 .