Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Hannah_Ahn
Group Title
prove the identity
csc theta over tan theta + cot theta = cos theta
 2 years ago
 2 years ago
Hannah_Ahn Group Title
prove the identity csc theta over tan theta + cot theta = cos theta
 2 years ago
 2 years ago

This Question is Closed

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

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

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

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
Sweet, thanks!
 2 years ago

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

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

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

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

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

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

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

Yifan12879 Group TitleBest ResponseYou've already chosen the best response.1
multiply the LHS by sinx cosx
 2 years ago

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
gotcha. sorry about that.
 2 years ago

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

Yifan12879 Group TitleBest ResponseYou've already chosen the best response.1
im sorry it should be theta...
 2 years ago

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

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

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

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

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
my 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
 2 years ago

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

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

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

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
i can't figure it out
 2 years ago

Yifan12879 Group TitleBest ResponseYou've already chosen the best response.1
which step?
 2 years ago

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

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

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

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

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

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
1 over cos x isn't same as cos x
 2 years ago

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
i got that too.
 2 years ago

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

Hannah_Ahn Group TitleBest ResponseYou've already chosen the best response.0
i 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.
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.