Christians4
Prove:
(sinx + cosx) (Tan^2x+1/tanx) = 1/cosx + 1/sinx
Picture below for what it looks like properly
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Christians4
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tell me if you need clarification i can drop LS and RS
Christians4
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yes your back!
lgbasallote
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hmm seems i really can't figure out what you mean. maybe it's time to show the picture
Christians4
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|dw:1352211230059:dw|
Christians4
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|dw:1352211285143:dw|
lgbasallote
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ahh
lgbasallote
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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
Christians4
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sec
Christians4
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I ended up getting (sinx+cosx) (1/cosxsinx) for my left side
Christians4
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woo it worked
Christians4
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How do I prove identities that are like this:
Christians4
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1+tanx/1-tanx = Tan (x+pi/4)
myininaya
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\[\frac{1+\tan(x)}{1-\tan(x)}=\tan(x+\frac{\pi}{4})\]
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)
Christians4
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sum identity for tan?
Christians4
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I know the cos and sin ones
Christians4
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is it just those over eachother?
Christians4
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oops im confused.
Christians4
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do u simply mean sinx/cosx?
phi
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try using tan = sin/cos and see how it works out
Christians4
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alright but on the R.S what do i do with the (x +pi/4)
myininaya
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\[\tan(x+\frac{\pi}{4})=\frac{\sin(x+\frac{\pi}{4})}{\cos(x+\frac{\pi}{4})}\]
Use sum identity for sine and cosine.
phi
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remember
sin(a+b)= sin(a)cos(b) + cos(a) sin(b)
and
cos(a+b)= cos(a)cos(b)- sin(a)sin(b)
Christians4
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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
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write down what you have so far
Christians4
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sinxcospi/4 +cpsxsinpi/4 / cospi/4cosx + sinpi/4sinx
phi
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pi/4 is 45º
it is good to have memorized cos(45) and sin(45)
Christians4
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oh i knew that but can i convert it in the eqqn?
Christians4
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so i could right 45deg instead of pi/4?
phi
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btw, notice that you have the wrong sign in the denominator
phi
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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
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just like 1 foot is the same as 12 inches
Christians4
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alright thanks
Christians4
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I think i got it, gotta head to class now, ill ask teacher if hes free
Christians4
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Thanks for your help