It is a quadratic equation in sin‌x, so D≥0 ⇒‌‌(3+a)2−4×4a≥0 ⇒‌‌9+a2+6a−16a≥0 ⇒‌‌a2−10a+9≥0 ⇒‌‌(a−1)(a−9)≥0 ⇒‌‌a≥9 or a≤−9 Now, at a=9, Eq. (i) becomes 9sin2x−12‌sin‌x+4=0 ⇒‌‌(3‌sin‌x−2)2=0 ⇒‌‌sin‌x=‌