The solution set of the system of equations `x+y=(2pi)/3,cosx+cosy=3/2 – InterviewSolution

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1.	The solution set of the system of equations `x+y=(2pi)/3,cosx+cosy=3/2,`where `xa n dy`are real, is ________
Answer» Correct Answer - No solution Given, ` x + y = ( 2pi)/(3)` ` and " " cos x + cos y = (3)/(2)` ` rArr cos x + cos (( 2pi)/(3) - x ) = (3)/(2)` `rArr cos x + (-(1)/(2) cos x + (sqrt3)/(2) sinx ) = (3)/(2)` ` rArr " " (1)/(2) cos x + (sqrt3)/(2) sinx = (3)/(2)` ` rArr sin ((pi)/(6) + x ) = (3)/(2)` , which is never possible. Hence, no solution exists.

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