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Question

The value a for which the equation 4cosec2(π(a+x))+a24a=0 has a real solution is:

A
a=1
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B
a=2
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C
a=3
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D
none of these
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Solution

The correct option is D a=2
4csc2(π(a+x))+a24a=0
[4csc2(π(a+x))4]+(a24a+4)=0
4(csc2(π(a+x))1)+(a2)2=0
(2cot((π(a+x)))2)+(a2)2=0
(a2)2=0a2=0a=2

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