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The set of values of a for which the equation $\cos 2 x + a \sin x = 3 a - 17$ possesses a solution is $[c, d]$ then d-c =

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Correct option is A

1−2sin2x+asinx=3a−17⇒2sin2x−asinx+3a−18=0⇒sinx=a±a2−83a−184 =a±a−124 =2a−124 or 3 =a−62Now −1≤a−62≤1 −2≤a−6≤2⇒4≤a≤8

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The set of values of a for which the equation cos2x+asinx=3a−17 possesses a solution is c,d then d-c =

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The set of values of a for which the equation $\cos 2 x + a \sin x = 3 a - 17$ possesses a solution is $[c, d]$ then d-c =