anonymous
  • anonymous
lim x-> pi/4 of (1-tanx)/(sinx-cosx)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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terenzreignz
  • terenzreignz
Did you try multiplying by conjugates?
anonymous
  • anonymous
No I multiplied by cosx?
terenzreignz
  • terenzreignz
Why, though?

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anonymous
  • anonymous
Because tanx becomes sinx/cosx so to cancel the denominator I multiplied by cos x so it becomes (cosx-sinx)/cosx•sinx-cosx and then the cosines equal 1 and as well do the sines so its -1/-cosx
anonymous
  • anonymous
But the answer is supposed to be -square root of 2 but I got positive and don't know what i did wrong
terenzreignz
  • terenzreignz
Fair enough, hang on.
terenzreignz
  • terenzreignz
\[\Large \lim_{x\rightarrow \frac \pi 4}\frac{1-\tan(x)}{\sin(x) - \cos(x)}\]
terenzreignz
  • terenzreignz
You missed a tiny detail, it would seem ^_^ \[\Large \frac{\cos(x)}{\cos(x)}\cdot \frac{1-\tan(x)}{\sin(x) - \cos(x)}= \frac{\cos(x)-\sin(x)}{\cos(x)[\sin(x) - \cos(x)]}\]
terenzreignz
  • terenzreignz
See it now? \[\LARGE = \frac{\cos(x) - \sin(x)}{\cos(x)[\cos(x) -\sin(x)]\color{red}{(-1)}}\]
anonymous
  • anonymous
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terenzreignz
  • terenzreignz
Because these two are negatives of each other: \[\LARGE\frac{\color{red}{\cos(x)-\sin(x)}}{\cos(x)[\color{blue}{\sin(x) - \cos(x)}]}\]
anonymous
  • anonymous
I'm new to this website but for some reason I can't see all of what you wrote
anonymous
  • anonymous
Where you put you missed a tiny detail I can't see the whole problem and where you put see it now as well
terenzreignz
  • terenzreignz
@Daisytoolovely sorry, was distracted... basically cos(x) - sin(x) = -[sin(x) - cos(x)] So that in effect, cos(x) - sin(x) / sin(x) - cos(x) = -1

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