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Number of integer values of n so that $\sin x (\sin x + \cos x) = n$ has at least one solution

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Correct option is C

We have sin2x+sinxcosx=n⇒1−cos2x2+12sin2x=n⇒sin2x−cos2x=2n−1⇒−2≤2n−1≤2 ∵ −2≤sin2x−cos2x≤2⇒−2+1≤2n≤2+1⇒−2+12≤n≤2+12 ⇒n=0,1

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Number of integer values of n so that sinx(sinx+cosx)=n has at least one solution

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Number of integer values of n so that $\sin x (\sin x + \cos x) = n$ has at least one solution