Be2lla Be2lla
  • 22-07-2022
  • Mathematics
contestada

2sin^2(x)+sin(2x)=2

please help!!

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subtomex0
subtomex0 subtomex0
  • 22-07-2022

[tex]2sin {}^{2} (x) + sin(2x) = 2 \\ 2sin {}^{2} (x) + 2sin(x)cos(x) = 2 \\ sin {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^{2} (x) + sin(x)cos(x) = 0[/tex]

[tex]cos(x)( - cos(x) + sin(x)) = 0[/tex]

[tex]cos(x) = 0 \\ x = \frac{\pi}{2} + k\pi \\ \\ sin(x) = cos(x) \\ x = \frac{\pi}{4} + k\pi[/tex]

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