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Number of integral values of ‘a’ satisfying the equation ${[\cos x]}^{2} + \cos x = 2 a$ is (where [ ] denotes G.I.F)

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Correct option is B

2a=cosx2+cosx, here a∈I⇒cosx∈I⇒cosx=−1 or 0 or 1⇒2a=cos2x+cosx= 0 or 2 ⇒ a= 0 or 1

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Number of integral values of ‘a’ satisfying the equation cosx2+cosx=2a is (where [ ] denotes G.I.F)

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Number of integral values of ‘a’ satisfying the equation ${[\cos x]}^{2} + \cos x = 2 a$ is (where [ ] denotes G.I.F)