For which values of a does the equation `4sin(x+pi/3)cos(x-pi/6)=a^2+sqrt(3)sin2x-cos2x` have solution? Find the solution for `a-0,a n ye xi s t sdot`

Explanation

The given equation can be rewritten as
`2[sin (2x+pi//6)+sin pi//2]=a^(2) +sqrt(3) sin 2x-cos 2x`
or `cos 2x=((a^(2)-2))/2`
or `2 cos^(2) x=a^(2)/2 or cos^(2) x=(a/2)^(2)` ...(i)
or `a^(2) le 4 or -2 le a le 2` ...(ii)
For `a=0` , the given equation is reduced to
`cos x =0`, i.e., `x=npi+(pi//2), n in Z` ...(iii)