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Question

General solution of the equation sin2x+cosec2x2(sinx+cosec x)+2=0 is
  1. (4n1)π2, nZ
  2. (2n1)π2, nZ
  3. (4n+1)π2, nZ
  4. (2n+1)π2, nZ


Solution

The correct option is C (4n+1)π2, nZ
sin2x+cosec2x2(sinx+cosec x)+2=0
(sin2x2sinx+1)+(cosec2x2cosec x+1)=0
(sinx1)2+(cosec x1)2=0
sinx1=0 and cosec x1=0
sinx=1 and cosec x=1
x=(4n+1)π2; where nZ 

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