Prove the following inequalities `1+cotx\ lt=cotx/2\ AA\ x in (0,pi)`

Prove the following inequalities 1+cot x<=cot(x)/(2)AA x in(0,pi)

Prove that following inequalities sinxlt=xlt=tanx\ AA\ in [0,pi/2]

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

027 Solve the following inequalities @) are cotx-5 arc cotx +6>0 (ii) arc sinx> arc cosx (iii) tan (arc sinx)>1

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

Evaluate the following integrals: int((1-cotx)/(1+cotx))dx

Evaluate the following integral: int_0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ )+sqrt(tanx))dx

Evaluate the following integral: int_0^(pi//2)1/(1+cotx)dx

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

Prove the inequalities 1 +1/2 x - (x^(2))/8 lt sqrt(1+x) lt 1 +1/2 x at 0 lt x lt oo