Question

How do you determine if `cot60^circ<cot75^circ` is true or false?

Answer 1

It's false

Explanation:

Recall that `d/dx(cotx) = -csc^2x`. If we convert to radians, we must prove whether or not

`cot(pi/3) < cot((5pi)/12)`

If you test within the derivative, you can see that at both these points the function is decreasing, and that since `-csc^2x` never equals `0` in the interval `[pi/3, (5pi)/12]`, cot(60˚) > cot(75˚)#, so the statement is false.

Hopefully this helps!