Determine the smallest positive value of `x` which satisfy the equation `sqrt(1+sin2x)-sqrt(2)cos3x=0`

Answer

`pi/16`

Explanation

`sqrt(1 + sin 2x) - sqrt2 cos 3x = 0`
or `sqrt(1 + sin 2x) = sqrt2 cos 3x`
or `1 + sin 2x = 2 cos^(2) 3x`
`1 + sin 2x = 1 + cos 6x`
or `cos ((pi)/(2) - 2x) = cos 6x`
or `(pi)/(2) - 2x = 2n pi -+ 6x`
`:. X = (npi)/(2) - (pi)/(8) or x = (npi)/(4) + (pi)/(16)`
We get smallest value when `n = 0 " then " x = pi//16`