Solve `sin^(4)x=1+tan^(8)x`.

Answer

No solution

Explanation

`sin^(4) x=1 + tan^(8) x`
Now, `1+tan^(8) x ge 1 and sin^(4) x le 1`
`rArr L.H.S.=R.H.S.`
Hence, for the given equation to be satisfied,
`sin^(4) x=1 and 1+ tan^(8) x=1`
`rArr sin^(2) x=1 and tan^(8) x=0`
which never possible, since `sin x` and `tan x` vanish simultaneously.
Therefore, the given equation has no solution.