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$\cos 2 x + a \sin x = 2 a - 7 p o s s e s s e s a s o l u t i o n f o r :$

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all a

a>6

a<2

a∈2,6

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detailed solution

Correct option is D

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

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

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$\cos 2 x + a \sin x = 2 a - 7 p o s s e s s e s a s o l u t i o n f o r :$