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Hannah_Ahn
 3 years ago
prove the identity
csc theta over tan theta + cot theta = cos theta
Hannah_Ahn
 3 years ago
prove the identity csc theta over tan theta + cot theta = cos theta

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Zed
 3 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ \frac{1}{sin {\theta}}}{tan{\theta}}+\frac{1}{tan{\theta}}=cos{\theta}\]

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0I am sorry, how did that happen?

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1Sorry I will write it up first and post it with steps. Just a moment

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1does it mean that (1/sin x)^2+(1/sin x)=1?

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1if you divide the cos theta from both sides

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0I still would appreciate to see the steps plz :s

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1but why? let x=pi/6 then 4+2=1??

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1yes I'm having that issue too. Are you sure it's written down right?

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0\[\csc \theta \over \tan \theta +\cot \theta\] = [\cos \theta\]

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1I see now, next time put the tan theta + cot theta in brackets to make it clearer.

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1multiply the LHS by sinx cosx

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0gotcha. sorry about that.

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1i mean csc x /(tan x + cot x)= cscx sinx cosx / (tanx sinx cosx+cotx sinx cosx)=cosx/(sin^2 x+cos^2 x)=cosx

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1im sorry it should be theta...

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0why did you multiply each sides by sinx cosx? how could u tell?

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1\[\frac{1/sin{\theta}}{tan{\theta}+1/tan{\theta}}=cos{\theta}\]\[1/sin{\theta}=tan{\theta}cos{\theta}+cos{\theta}/tan{\theta}\]\[1/sin{\theta}=sin{\theta}+cos^2{\theta}/sin{\theta}\]\[1/sin{\theta}=sin^2{\theta}/sin{\theta}+cos^2{\theta}/sin{\theta}\]\[1/sin{\theta}=1/sin{\theta}\]\[1=1\]

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1Here's a different way to go about it :)

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1because there are sinx cosx in the denominator

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0my teacher doesn't let me combite the left side and the right side.. in this case i would need to make the left side cos theta. :S

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0zed; yur way is something to think about, and it's cool. yet i won't b able to use your method

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1@Zed you shouldnt give out a prove like this, you should write LHS=...=....=...=RHS

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0yifian; i don't really get how you got there.. :(

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i can't figure it out

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0is there other way to do it?

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1Thanks Yifan, I haven't done proof in a long time. \[LHS = \frac{1/sinx}{sinx/cosx+cosx/sinx}\] \[=\frac{1/sinx}{(sin^2x+cos^2x)/sinxcosx}\]\[=\frac{1/sinx}{1/sinxcosx}\]\[=\frac{1}{cosx}\]\[=RHS\]

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1sorry that second last line was supposed to be cosx

Yifan12879
 3 years ago
Best ResponseYou've already chosen the best response.1yeah that is a good prove except that you substitute theta for x..

Zed
 3 years ago
Best ResponseYou've already chosen the best response.1yeah i got tired of writing theta out

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.01 over cos x isn't same as cos x

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0well thanks for your time :)

Hannah_Ahn
 3 years ago
Best ResponseYou've already chosen the best response.0i still don't get it . for some reason, im very confused. i will ask my teacher and I will let you know if there is a simpler way to do it if you are interested :P g'nite.
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