# trig verifying identities

• Apr 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)
• Apr 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)
• Apr 27th 2008, 06:43 PM
elizsimca
I think I screwed it up..so nevermind..go with what the genius mathstud says!! :)
• Apr 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
• Apr 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!!
• Apr 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)
• Apr 27th 2008, 07:03 PM
angelkat007
so would the 2nd one be (cos^2 x)(sin^2 x)???
Thanks so much for your help!
• Apr 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!
• Apr 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 :)
• Apr 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