Correct Answer - A
The given equation is
`3 (sin x + cos x)-2 (sin x+ cos x) (1- sin x cos x)=8`
or `(sin x+cos x) [3-2+2 sin x cos x]=8`
or `(sin x+cos x)[sin^(2) x+cos^(2) x+2 sin x cos x]=8`
or `(sin x+ cos x)^(3)=8`
or `sin x + cos x =2`
or `sin x, cos x=1`, which is not possible. Hence, the given equation has no solution.