The set of values of ‘a’ for which the equation cos2x+asinx=2a−7 possesses a solution is c,d, then c+d=

We have cos2x+asinx=2a−7⇒1−2sin2x+asinx=2a−7⇒2sin2x−asinx+2a−8=0⇒sinx=a±a2−8(2a−8)4=a±(a−8)24⇒sinx=a±(a−8)4=2a−84     or    2Now −1≤sinx≤1⇒−1≤2a−84≤1⇒−4≤2a−8≤4⇒4≤2a≤12⇒2≤a≤6∴c=2,d=6⇒c+d=8