show that : ` x- x^3/6 lt sinx ` for `0 lt x lt pi/2`

If 0 lt x lt pi/2 then

If 0 lt x lt pi/2 then

If 0 lt x lt pi /2 then

Show that 2 sin x + tanx ge 3x , where 0 le x lt (pi)/(2)

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

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

Find the values of A and B if the following function is continuous on [-pi,pi]. f(x) = {((2sinx-sin2x)/x^3,; -pi lt= x lt 0), (Asinx + B cosx,; 0 lt= x lt= pi/2), ((cosecx-1)/(pi//2-x)^2,; pi/2 lt x lt= pi):}

The value of int _(pi//4) ^(pi//3) cosec x d (sin x ) for 0 lt x lt pi //2 is