If `=lt=xlt=2pi,` then the number of solutions of `3(sinx+cosx)-(sin^3x+cos^3x)=8` is 0 (b) 1 (c) 2 (d) 4

Options

A. 0
B. 1
C. 2
D. 4

Answer

A

Explanation

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.