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a quadratic equation whose roots are cosec 2 theta and sec 2 theta can be x^2-2x+2=0 x^2-3x+3=0 x^2-5x+5=0 none

a quadratic equation whose roots are cosec2 theta and sec2 theta can be 
  • x^2-2x+2=0
  • x^2-3x+3=0
  • x^2-5x+5=0
  • none

Grade:12

1 Answers

Ketan Prakash
31 Points
5 years ago
Sec2a+cosec2a=1/sin2a+1/cos2a
=sin2a+cos2a/sin2acos2a=4/sin22a
 
Sin2a=2sina cos a
Sina cosa = 1/2 sin2a
 
Sum of the roots = 4/sin22a  > or = 4
 
Products of roots = 4/sin22a > or equals to 4
 
Both sum of roots and prouct of roots are equal.let it t.
 
Hence , equation will be x2 - tx + t=0  (t always greater or equals to 4)
 
Hence , x2-5x+5=0 is one of the solution.

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