Solve the following equations:
(i) `sin^(8)x - cos^(8)x=1`
(ii) `sin^(10)x - cot^(8)x=1`

Explanation

(i) `sin^(8)x = 1+ cos^(8)x`
as `0 le sin^(8)x le 1` and `1 le 1 + cos^(8)x le 2`
Hence solution is obtained when both sides are equal to 1.
If `sin^(8)x =1 rArr x = npi +-pi/2, n int Z`
`1+ cos^(8)x=1 rArr x = mpi +-pi/2, m int Z`
`rArr` Common soltion may be written as `x = kpi +- pi/2, k int Z`
(ii) `sin^(10)x= 1+cot^(8)x`
But `0 le sin^(10)x le 1`
and `1+ cot^(8)x ge 1`
Hence solution is obtained when both sides are equal to 1.
`rArr sin^(10)x = 1+ cot^(8)x=1`
`rArr x=npi + pi/2, n int Z`