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 Posted: Tue Oct 07, 2008 5:12 pm
So Like I Am Having Problems proving why some trig functions are equal and I Need Help so yeah. Here are the problems.
TanX+CotX=CscX*SecX
SinX+CotX*CosX=CscX
TanX(SinX+CotX*Cosx)=SecX
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Posted: Tue Oct 07, 2008 5:46 pm
Also CosX(SinX + CosX*Cscx*CscX)=CscX*CscX
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Posted: Tue Oct 07, 2008 5:53 pm
OMG! I remember these. but I CANNOT for the life of me remember the conversions. I'm going to look them up and see if I can help. It might take a little while.
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Posted: Tue Oct 07, 2008 6:23 pm
Okay... it's been a REALLY LONG TIME since I was in precalc, but if I remember right, there was no calculus in there... so that means that the tools you're expected to use are slim... o.o
So, most of those, you could probably convert into sines and cosines (eg: Tan = sin/cos, cot = cos/sin, Csc = 1/sin, Sec = 1/cos, or so), then algebraically manipulate the equations to make them work...
Er... that's about all that I can think of, that would work... o.o
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Posted: Tue Oct 07, 2008 6:28 pm
Sibeiko Okay... it's been a REALLY LONG TIME since I was in precalc, but if I remember right, there was no calculus in there... so that means that the tools you're expected to use are slim... o.o So, most of those, you could probably convert into sines and cosines (eg: Tan = sin/cos, cot = cos/sin, Csc = 1/sin, Sec = 1/cos, or so), then algebraically manipulate the equations to make them work... Er... that's about all that I can think of, that would work... o.o Thats what I was trying to do I cant get those to get down right. I am really confused. :d
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Posted: Tue Oct 07, 2008 7:23 pm
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Posted: Tue Oct 07, 2008 7:32 pm
1st one:
tanX+cotX=cscX(secX)
First look at the right side-- cscX= 1/sinX and secX= 1/cosX so when multiplied the right side gives you 1/(sinXcosX) and it's in the simplest form
Now, look at the left side. TanX= sinX/cosX and cotX= cosX/sinX
In order to add, you have to have common denomanators, so you multiply sinX/cosX by sinX/sinX and cosX/sinX by cosX/cosX
(I'm going to drop the X's, but they're still there, okay?)
giving you the fractions: sin(squared)X/cosXsinX + cos(squared)X/cosXsinX
or sin^2+ cos^2/sincos
sin^2+cos^2=1, so the left side equals 1/sincos, and the right side equals 1/sincos.
Make sense?
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Posted: Tue Oct 07, 2008 7:41 pm
DO you need me to help you with the rest?
ANd are you sure the 4th one was copied right?
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Posted: Tue Oct 07, 2008 7:42 pm
Yeah I still need help and..I did copy the fourth one wrong XD.
Cosx(Secx+CosxCscx(squared)=Cscx(squared)
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Posted: Tue Oct 07, 2008 7:57 pm
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Posted: Tue Oct 07, 2008 8:02 pm
All I need know is the last. I cant figure it out
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Posted: Tue Oct 07, 2008 8:08 pm
The third one is pretty simple
Leaving off the X's again, by the way
Tan(sin+cotcos) = sec
So work on the more complicated side first, which would be the left side
1) tan= sin/cos
2) cot=cos/sin, so it's (cos/sin)(cos/1) which turns into cos^2/sin
3) you now have cos/sin (sin/1 + cos^2/sin) so you need to get a common denomanator so you can add, so you multiply the sin/1 by sin/sin so you get sin^2/sin + cos^2/sin
4) Add the two together, and you get sin^2+cos^2/sin
5) sin^2+cos^2=1, so you can substitute it in
6) the left side now looks like: sin/cos(1/sin)
7) multiply it through so you have sin/sincos
cool the sin's cancel leaving you with 1/cos
9) look at the right side-- sec
10) sec= 1/cos
so they are now equal
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Posted: Tue Oct 07, 2008 8:09 pm
Amigox3 All I need know is the last. I cant figure it out So I didn't see this until after I posted the 3rd one, so I'll work on the 4th one now
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Posted: Tue Oct 07, 2008 8:12 pm
Okay, got the fourth one. I'll write it out now
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Posted: Tue Oct 07, 2008 8:23 pm
You start with cos(sec+coscsc^2)= csc^2
Start with the left side again, work inside the parenthesis first
sec= 1/cos, scs^2= 1/sin^2
so it looks like: [1/cos+ cos(1/sin^2)]
then multiply the cos and the 1/sin^2, so it looks like: 1/cos + cos/sin^2
Then, find a common denominator, by multiply the first term by sin^2/sin^2, and the second term by cos/cos, so you end up with:
sin^2/sin^2cos + cos^2/sin^2cos
add the fractions now, so you get sin^2+cos^2/sin^2cos
sin^2+cos^2=1, substitute in, so you get 1/sin^2cos
so your left side looks like this now: cos(1/sin^2cos)
Multiply in the cos, and simplify:
cos/sin^2cos or 1/sin^2
THen go for the right side of the equation: csc^2
csc^2= 1/sin^2
so the sides are equal
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