This will be true if
nx = -[pi/2 - mx]
= mx - pi/2
(m - n)x = pi/2
x = (pi/2)/(m-n)
Check: suppose m = 3 and n = 1
Then x = pi/4
tan 3pi/4 =? -cot pi/4
-1 = -1
Solve the equations for value of x
tan mx + cot nx = 0
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