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

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

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Answer 1 · 2018-04-21T13:58:16

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.

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

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