Show that `cot(pi/4+x)cot(pi/4-x)=1`

cot((pi)/(4)-x)+cot((pi)/(4)+x)=4

Prove that cot((pi)/(4) + 0) cot ((pi)/(4) - 0) =1 .

Prove that cot((pi)/(4)-2cot^(-1)3)=7

cot(-15pi)/(4)

Show that the function f(x)=cot^(-1)(sin x+cos x) is decreasing on (0,pi/4) and increasing on (pi/4,pi/2)

If A+B=(pi)/(4), show that (cot A-1)(cot B-1)=2

1. If A+B=(pi)/(4), show that (cot A-1)(cot B-1)=2

The value of int_(0)^((pi)/(4))ln cos((pi)/(4)+x)^(cot((pi)/(4)-x))dx is

Show that f(x)=tan x-cot x-x+pi/4+1 if: f'(x)=sec^2x+cosec^2x-1 and f(x)=1, when x=pi/4 .

Prove that: cos((3 pi)/(2)+x)cos(2pi+x)[cot((3 pi)/(2)-x)+cot(2 pi+x)]=1