Eliminate x ! DOUBT !

Cosec x - Sin x =m
Sec x - Cos x =n

Please Solve It In Detail !!

2 Answers

cos²x=msinx
sin²x=ncosx
so sin⁴x=n²msinx
so, sin³x=n²m
cos³x=m²n
so
(n^{2}m)^{2/3}+(m^{2}n)^{2/3}=1

In The Answer There is
(m²n)^23 +(n²m)^23 = 1
=m²n²(m²+n²+3)

How do we get the last part ??

m²n²(m²+n²+3)=1

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