find the value of the

Options

A. `pm sqrt(n pi), n in {0, 1, 2, ...}`
B. `pm sqrt(n pi), n in {1, 2, ...}`
C. `pi/2+2npi, n in {..., -2, -1, 0, 1, 2 ...}`
D. `2npi, n in {..., -2, -1, 0, 1, 2, ...}`

Answer

A

Explanation

`(fogogof) (x)= sin^(2) (sin x^(2))`
`(gogof) (x) = sin (sin x^(2))`
`:. Sin^(2) (sin x^(2))= sin (sin x^(2))`
`rArr sin (sin x^(2)) [sin (sin x^(2))-1]=0`
`rArr sin (sin x^(2))=0` or `1`
`rArr sin x^(2) = npi` or `2 mpi+pi//2`, where `m, n in I`
`rArr sin x^(2)=0`
`rArr x^(2) =n pi rArr x= pm sqrt(npi), n in {0, 1, 2, ...}`.