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Find the value of a for which the eqn 4 cosec 2 (π (a+x) ) + a 2 - 4a = 0 has a real solution.

Find the value of a for which the eqn 


4 cosec 2 (π (a+x) ) + a2 - 4a = 0 has a real solution.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Sanchit

4 cosec 2 (π (a+x) ) + a2 - 4a = 0

4 cosec 2 (π (a+x) ) =- a2 + 4a 

L .H .S is always greater than 4 so for real solution

 -a2 + 4a ≥4

or (a-2)2≤0

so only a=2 is possible


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