Detrich813 Detrich813
  • 18-05-2017
  • Mathematics
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Solve 2 cosx - sin²x + 2 =0 for all values of x.

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LammettHash
LammettHash LammettHash
  • 18-05-2017
[tex]2\cos x-\sin^2x+2=0[/tex]
[tex]2\cos x-(1-\cos^2x)+2=0[/tex]
[tex]\cos^2x+2\cos x+1=0[/tex]
[tex](\cos x+1)^2=0[/tex]
[tex]\cos x+1=0[/tex]
[tex]\cos x=-1[/tex]
[tex]\implies x=\pi+2k\pi[/tex]

where [tex]k[/tex] is an integer.
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