Which of the following set of values of `x` satisfies the equation `2^(2sin^(2x+1))+2^(2sin^(2x+3sinx))=9?` `x=npi+-pi/6,n in I` (b) `x=npi+-pi/3, n in I` `x=npi,n in I` (d) `x=2npi+pi/2,n in I`

Options

A. `x=n pi pm pi/6, n in I`
B. `x= n pi pm pi/3, n in I`
C. `x=n pi, n in I`
D. `x=2n pi +pi/2, n in I`

Answer

A, D

Explanation

`2^((2sin^(2)x-3 sin x+1))+2^(3-(2 sin^(2)x-3 sin x+1))=9`
Let `2^((2 sin^(2)x-3 sin x+1))=t`
`rArr t+8/t=9` or `t^(2) -9t+8=0`
or `t=1, 8`
`rArr 2 sin^(2) x-3 sin x+1=3`
or `2 sin^(2) x-3 sin x+1=0`
`rArr sin x = -1/2, sin x = 1/2, sin x =1`