Q.

The difference of the maximum and the minimum values of the function  5 cosx+3  cos(x+π3)+8  over R is

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a

16

b

14

c

7

d

15

answer is B.

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Detailed Solution

5cosx+3cosx2−32sinx+8=  132cosx−332sinx+8Whose minimum and maximum values are              8−1322+3322     and      8+1322+3322=1    and     15∴Maximum – minimum = 15 – 1 = 14
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The difference of the maximum and the minimum values of the function  5 cosx+3  cos(x+π3)+8  over R is