Solve `(sin^3x/2-cos^3x/2)/(2+sinx)=(cosx)/3`

Explanation

`("sin"^(3) x/2-"cos"^(3)x/2)/(2 + sin x)=(cos x)/3`
or `(("sin"x/2-"cos"x/2)(1+"sin"x/2"cos"x/2))/(2(1+"sin" x/2"cos"x/2))=(cos x)/3`
or `"sin"x/2-"cos"x/2=2/3 cos x`
or `1-sin x=4/9 cos^(2) x` (On squaring)
or `4/9 sin^(2) x-sin x+1-4/9=0`
or `4 sin^(2) x-9 sin x+5=0`
or `(4 sin x-5) (sin x -1)=0`
or `sin x=1`
`rArr x=2 npi+pi/2, n in Z`