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Question

Question: The maximum value of 4sin<sup>2</sup> x + 3cos<sup>2</sup>x + \(\sin\frac{x}{2} + cos\frac{x}{2}\)is...

The maximum value of 4sin2 x + 3cos2x + sinx2+cosx2\sin\frac{x}{2} + cos\frac{x}{2}is

A

4+24 + \sqrt{2}

B

3+23 + \sqrt{2}

C

9

D

4

Answer

4+24 + \sqrt{2}

Explanation

Solution

Maximum value of 4sin2x + 3cos2x i.e. sin2x + 3 is 4 and that of sinx2\frac{x}{2}+ cosx2\frac{x}{2}= 2\sqrt{2}, both attained at

x = π/2.

Hence the given function has maximum value4+24 + \sqrt{2}