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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${(csc x - cot x)}^{4} {(csc x + cot x)}^{4} = 1$ $(cscx-cotx)^4(cscx+cotx)^4=1$

${((csc x - cot x) (csc x + cot x))}^{4} = 1$ $((cscx-cotx)(cscx+cotx))^4=1$

${({csc}^{2} x - {cot}^{2} x)}^{4} = 1$ $(csc^2x-cot^2x)^4=1$

${csc}^{2} x - {cot}^{2} x = \pm 1$ $csc^2x-cot^2x=+-1$

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

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