bewellplus.gsu.edu
aviationfan aviationfan
  • 24-05-2015
  • Mathematics
Answered

How to solve these equations?

\(
1) sin^2x+|sinx|-2=0
\)

\(
2) |sinx| = cos2x\)

Verified Answer :

crisforp
crisforp crisforp
  • 24-05-2015

1) / sin x / = y ≥ 0 ;
   We solve the equation \(y^{2} +y - 2 = 0 ;\)
a = 1 ; b = 1 ; c = - 2 ;
\(b^{2} - 4ac = 9 ;\)
y1 = ( - 1 + 3 ) / 2 = 1 ≥ 0 ( correct ) ;
y2 = ( - 1 - 3 ) / 2 = - 2 ≥ 0 ( false ) ;
Then, / sin x / = 1 ;
sinx = + 1 or sin x = - 1 ;
x ∈ { 90 }  U { 270 } ;
x ∈  {90 , 270}.

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