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Question

If 4cos2θ+15cosθ4=0, find the value of (log2cosθ)5:

A
1
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B
132
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C
1
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D
none of these
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Solution

The correct option is D 132
Given 4cos2θ+15cosθ4=0
4cos2θ+16cosθcosθ4=0
4cosθ(cosθ+4)1(cosθ+4)=0
(4cosθ1)(cosθ+4)=0
cosθ=14,4cosθ=14
So (log2cosθ)5=(log222)5=(2)5=132

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