trig verifying identities

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April 27th 2008, 06:39 PM
angelkat007

trig verifying identities

I'd really appreciate it if someone could help me with these 2 problems!

1) Verify the identity:

Cosx/(1-sinx) = (1+sinx)/Cosx

2) Simplify and express without fractions:

(1-sin^2x)/(cot^2x+1)
April 27th 2008, 06:41 PM
Mathstud28

Quote:

Originally Posted by angelkat007

I'd really appreciate it if someone could help me with these 2 problems!

1) Verify the identity:

Cosx/(1-sinx) = (1+sinx)/Cosx

2) Simplify and express without fractions:

(1-sin^2x)/(cot^2x+1)

For the second one use the identities $1-\sin^2(x)=\cos^2(x)$
and $\csc^2(x)=1+\cot^2(x)$

as for the first one I would suggest multiplying both sides by cos(x)
April 27th 2008, 06:43 PM
elizsimca

I think I screwed it up..so nevermind..go with what the genius mathstud says!! :)
April 27th 2008, 06:47 PM
Mathstud28

Quote:

Originally Posted by elizsimca

2.

$\frac{1-\sin^2{x}}{\cot^2{x}+1}$ = $(1-\sin^2{x})(\tan^2{x}+1)$ = $(\cos^2{x})(\sec^2{x})$ = $\frac{\cos^2{x}}{\cos^2{x}}$ = $1$

I think..confirmation anyone?

EDIT

I think it's wrong..

Dang!

Everything is right based off your first assumption..but unfortunately that assumption is wrong...(Crying)...its ok though! at least you saw it was wrong...we all make mistakes..me ESPECIALLY included...ask anyone...I probably should get the award for most typos/clerical errors
April 27th 2008, 06:48 PM
elizsimca

Yeah, I realized shortly after....

Forum 1 Elizsimca 0

Oh, and mathstud, I like how you brought me down gently....

"Everything is right based off your first assumption..but unfortunately that assumption is wrong.."...haha, made me laugh!!
April 27th 2008, 06:53 PM
Mathstud28

Quote:

Originally Posted by elizsimca

Yeah, I realized shortly after....

Forum 1 Elizsimca 0

Oh, and mathstud, I like how you brought me down gently....

"Everything is right based off your first assumption..but unfortunately that assumption is wrong.."...haha, made me laugh!!

Haha...Tough Love Elizsimca...tough love...the key to growth :p

You seem to be a neo-denizen of MHF....its part of the process...well...I am also a new-comer...I still catch flack all the time (Rofl)
April 27th 2008, 07:03 PM
angelkat007

so would the 2nd one be (cos^2 x)(sin^2 x)???
Thanks so much for your help!
April 27th 2008, 07:04 PM
Mathstud28

Quote:

Originally Posted by angelkat007

so would the 2nd one be (cos^2 x)(sin^2 x)???
Thanks so much for your help!

(Clapping)..yes...good job!
April 27th 2008, 07:05 PM
elizsimca

Quote:

Originally Posted by angelkat007

so would the 2nd one be (cos^2 x)(sin^2 x)???
Thanks so much for your help!

Yeah, that's the answer my ti-89 gave me :)
April 27th 2008, 07:06 PM
Mathstud28

Quote:

Originally Posted by elizsimca

Yeah, that's the answer my ti-89 gave me :)

Ahh...the TI-89...the greatest thing ever...I ♥ my TI-89