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The maximum value of 4sin^2 x + 3cos^2x + sin x/2 + cos x/2 is

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The maximum value of 4sin2 x + 3cos2x + sin x/2 + cos x/2 is

(A)  4 + √2

(B)  3 + √2

(C)  9

(D)  4

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Correct option (A)  4 + √2

Maximum value of 4sin2x + 3cos2x, that is, sin2x + 3 is 4 and that of sin x/2 + cosx/2 is 1/√2 + 1/√2 = √2,both attained at x = π/2. Hence, the given function has the maximum value 4 + √2 .

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