Question

Prove that (tanx-cot)^2>=0 ?

Answer 1

Note that this question is not really related to trigonometry; rather, for any real number `a` then

`a^2>=0`

For any value of `a`:

`{(1^2=1>0),(3^2=9>0),((-1)^2=1),(0^2=0) :}`

The inequality below is easily proven by this.

`(tanx-cotx)^2>0`

If you're wondering, the equality only holds when `tanx=cotx`; this equation has infinitely many solutions, all of the form

`x=pi/4+kpi`, `k in ZZ`.