Solve `2^(cos 2x)+1=3.2^(-sin^(2) x)`

Answer

`x=n pi, n in Z or x=n pi pm pi/2, n in Z`

Explanation

`2^(cos 2x)+1=3.2^(- sin^(2)x)`
`rArr 2^(1-2 sin^(2) x)+1=3.2^(- sin^(2) x)`
Let `2^(- sin^(2) x)=t`
Now, given equation reduces to
`2t^(2)+1=3t`
`rArr t=1 and t=1//2`
If `t=1` then `sin^(2) x=0`
`rArr x=npi, n in I`
If `t=1/2` then `sin^(2) x=1`
`rArr x=npi pm pi/2, n in I`.