Respuesta :

assuming cos2 x means cos^2 x, u can substitute y=cosx and the equation becomes: y^2 + 2y -2 =0

solving it gives the solution -1+-sqrt(3)
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Answer:

Option D. 1

Step-by-step explanation:

Thinking process:

Let the quadratic equation be given by the formula:

[tex]cos^{2} x+ 2 cosx - 2 = 0[/tex]

then solving the equation using the factorization method:

using the trigonometry identity of cos 2x

then

[tex]Cos2x = 2cos^{2}x - 1[/tex]

Substituting 2Cos²x - 1 gives:

2[tex]cos^{2} x-1+cos^{2}x-2= 0[/tex]

rearranging gives:

[tex]3cos^{2}x = 3\\ cosx = \sqrt{1} \\ = 1[/tex]

hence cosx = 1

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