How do you solve (cscx-cotx)^4(cscx+cotx)^4=1?

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Answer 1 · 2018-06-10T00:15:08

Infinite solutions

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#(cscx-cotx)^4(cscx+cotx)^4=1#

#((cscx-cotx)(cscx+cotx))^4=1#

#(csc^2x-cot^2x)^4=1#

#csc^2x-cot^2x=+-1#

#csc^2x-cot^2x=1. :. csc^2x=1+cot^2x#, Infinite solutions

#csc^2x-cot^2x=-1, :. 1+cot^2x-cot^2x=-1#, no solution