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Question

The range of the function f(x)=5cosx+3cos(x+π/3)+4 is :

A
[3,11]
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B
[18,10]
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C
[10,18]
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D
None of these
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Solution

The correct option is A [3,11]
A]5cosx+3cos(x+π3)+4
=5cosx+3(cosxcosπ3sinxsinπ3)+4
5cosx+3(cosx2sinx32)+4
=132cosx332sinx+4
Let 132=a332=b
=acosxbsinx+4
max value =a2+b2+4
= (132)2+(332)2+4
=169+274+4=1964+4=142+4
=222=11
min value (1424)=3


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