anonymous
  • anonymous
solve 2secx+tanx=3 on the interval xE[0,2pi]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
this is a pain.
anonymous
  • anonymous
we have \[\frac{2}{\cos(x)}+\frac{\sin(x)}{\cos(x)}=\frac{2+\sin(x)}{\cos(x)}=3\] so \[2+\sin(x)=3\cos(x)\] \[3\cos(x)-\sin(x)=2\] \
anonymous
  • anonymous
now we have to write \[3\cos(x)-\sin(x)\] as a single function of sine, we get something like \[\sqrt{10}\sin(x+\tan^{-1}(3))\]

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anonymous
  • anonymous
no that is a mistake
anonymous
  • anonymous
\[-\sqrt{10}\sin(x-\tan^{-1}(3))=2\] i think it is right now
anonymous
  • anonymous
i wonder if there is an easier way, but i don't see it. you can divide by \[-\sqrt{10}\]and take the inverse sine of the result
anonymous
  • anonymous
let me try something else
anonymous
  • anonymous
no just going around in circles. the above will do it. do you have another method you are supposed to use?

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