cos2x+asinx=2a−7 possesses  a  solution  for:

We have cos2x+asinx=2a−7⇒1−2sin2x+asinx=2a−7⇒2sin2x−asinx+2a−8=0⇒sinx=a±a2−16a−44                      = a±a−84⇒ sinx=a−42 (or) 2Since sinx≠2, we have sinx=a−42Now      −1≤sinx≤1 ⇒   −1≤a−42 ≤1⇒        2≤a≤6