anonymous
  • anonymous
If (2tan(x))/(1-tan^2(x))=1, then what can x equal? My options are: A. x=7pi/8+npi B. x=pi/8+npi C. x=3pi/8+npi D. x=5pi/8+npi
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think that B is right but I don't know about any others. Can anybody help me?
anonymous
  • anonymous
I got the question wrong, but I still want to know how to do this!
anonymous
  • anonymous
\[\frac{ 2\tan x }{ 1-\tan ^2x }=1\] \[\tan 2x=1=\tan \left( \frac{ \pi }{ 4 }+n \pi \right)\] \[x=\left( \frac{ \pi }{ 8 }+n \frac{ \pi }{ 2 } \right)\]

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anonymous
  • anonymous
How did you go between the last two steps?
anonymous
  • anonymous
\[\tan 2 x=\frac{ \sin 2x }{ \cos 2x }=\frac{ 2\sin x \cos x }{ \cos ^2x-\sin ^2x }\] divide the numerator and denominator by \[\cos ^2x\] \[\tan 2x=\frac{ 2\tan x }{ 1-\tan ^2x }\]
anonymous
  • anonymous
\[\tan 2x=1=\tan \frac{ \pi }{ 4 }=\tan \left( \frac{ \pi }{ 4 }+n \pi \right)\] \[2x=\frac{ \pi }{ 4 }+n \pi,x=?\]
anonymous
  • anonymous
So that's \[1/8\pi +1/2n \pi ?\]
anonymous
  • anonymous
correct ,i have written above.
anonymous
  • anonymous
Okay I get it thank you. That helps a lot.
anonymous
  • anonymous
You can have a medal :)
anonymous
  • anonymous
yw
anonymous
  • anonymous
can you help me with another problem? @surjithayer
anonymous
  • anonymous
I have \[\cos(\pi/4)\cos(\pi/6)=1/2( (blank) \pi/12+\cos(5\pi/12)\]
anonymous
  • anonymous
\[2 \cos A \cos B=\cos \left( A+B \right)+\cos \left( A-B \right)\] \[\cos A \cos B=\frac{ 1 }{ 2 }\left\{ \cos \left( A+B \right)+\cos \left( A-B \right) \right\}\]

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