anonymous
  • anonymous
Prove: (sinx + cosx) (Tan^2x+1/tanx) = 1/cosx + 1/sinx Picture below for what it looks like properly
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
tell me if you need clarification i can drop LS and RS
anonymous
  • anonymous
yes your back!
lgbasallote
  • lgbasallote
hmm seems i really can't figure out what you mean. maybe it's time to show the picture

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anonymous
  • anonymous
|dw:1352211230059:dw|
anonymous
  • anonymous
|dw:1352211285143:dw|
lgbasallote
  • lgbasallote
ahh
lgbasallote
  • lgbasallote
here's a hint that might help: \[\huge \tan^2 x + 1 = \sec^2 x\] and \[\huge \sec^2 x = \frac1{\cos^2 x}\] try solving it
anonymous
  • anonymous
sec
anonymous
  • anonymous
I ended up getting (sinx+cosx) (1/cosxsinx) for my left side
anonymous
  • anonymous
woo it worked
anonymous
  • anonymous
How do I prove identities that are like this:
anonymous
  • anonymous
1+tanx/1-tanx = Tan (x+pi/4)
myininaya
  • myininaya
\[\frac{1+\tan(x)}{1-\tan(x)}=\tan(x+\frac{\pi}{4})\] I would write each side so that the function tan( ) only contains x and not both x & x+pi/4. You the sum identity for tan. If you don't know it write both sides in terms of sine and cosine. Use the sum identities for them to expand tan(x+pi/4)
anonymous
  • anonymous
sum identity for tan?
anonymous
  • anonymous
I know the cos and sin ones
anonymous
  • anonymous
is it just those over eachother?
anonymous
  • anonymous
oops im confused.
anonymous
  • anonymous
do u simply mean sinx/cosx?
phi
  • phi
try using tan = sin/cos and see how it works out
anonymous
  • anonymous
alright but on the R.S what do i do with the (x +pi/4)
myininaya
  • myininaya
\[\tan(x+\frac{\pi}{4})=\frac{\sin(x+\frac{\pi}{4})}{\cos(x+\frac{\pi}{4})}\] Use sum identity for sine and cosine.
phi
  • phi
remember sin(a+b)= sin(a)cos(b) + cos(a) sin(b) and cos(a+b)= cos(a)cos(b)- sin(a)sin(b)
anonymous
  • anonymous
I plugged in the sum identity but i dont know what do to next I have sin and cosx's which i dont know what to do with
phi
  • phi
write down what you have so far
anonymous
  • anonymous
sinxcospi/4 +cpsxsinpi/4 / cospi/4cosx + sinpi/4sinx
phi
  • phi
pi/4 is 45º it is good to have memorized cos(45) and sin(45)
anonymous
  • anonymous
oh i knew that but can i convert it in the eqqn?
anonymous
  • anonymous
so i could right 45deg instead of pi/4?
phi
  • phi
btw, notice that you have the wrong sign in the denominator
phi
  • phi
pi/4 and 45 mean the same thing.... it matters when using a calculator, or in certain math operations where radians are more useful... but the cos(45º) = cos(pi/4 radians)
phi
  • phi
just like 1 foot is the same as 12 inches
anonymous
  • anonymous
alright thanks
anonymous
  • anonymous
I think i got it, gotta head to class now, ill ask teacher if hes free
anonymous
  • anonymous
Thanks for your help

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