Precalculus/Trigonometry Halp Pls
Herro, so I have a doozy of a question here regarding verifying trigonometric identities.
I've been trying repeatedly to make the left side into the right, but I can't. I've tried Pythagorean Identities, Reciprocal Identities, I just don't exactly know what to do at this point. This is a very important question that I can't skip: The grading on this assignment is tweaked very oddly, the question alone is worth 3 homework assignments.
This is Mr. Question:
(1-cosx)/(1+cosx)=(cotx-cscx)^2
Thanks in advance for any help, I really appreciate it. c:
January 10, 2013
11 Comments • Newest first
@Above Using yours as reference though ^_^
(1-cos(x))/(1+cos(x))=(cot(x)-cosec(x))²
LHS=(1-cos(x))/(1+cos(x))
=(1-cos(x))²/((1+cos(x))(1-cos(x)))
=(1+cos²(x)-2cos(x))/(1-cos²(x))
=(1+cos²(x)-2cos(x))/sin²(x)
=(1/sin²(x))-(2cos(x)/sin²(x))+(cos²(x)/sin²(x))
=cosec²(x)-2cot(x)cosec(x)+cot²(x)
=(cosec(x)-cot(x))²
=RHS
EDIT: Too slow...dammit...
USA, 10th
[quote=Pwnagewafflez]Oh my god. Thank you SO much. I CAN FINALLY BE DONE! YOU HAVE RELEASED ME FROM MY PRISON. <3[/quote]
Just a question, what country are you in and what grade?
Oh my god. Thank you SO much. I CAN FINALLY BE DONE! YOU HAVE RELEASED ME FROM MY PRISON. <3
(1-cosx)/(1+cosx)=(cotx-cscx)^2
(1-cosx)/(1+cosx)=cot^2x - 2cotxcscx + csc^2x
=(csc^2x - 1) - 2cotxcscx + csc^2x
=2csc^2x - 1 - 2(sinx/cosx)(1/sinx)
=2csc^2x - 1 - 2/cosx
=2/sin^2x - 1 - 2/cosx
=2/(1-cosx) - 1 - 2/cosx
I give up, too tired
LHS: Multiply top and bottom by (1-cos(x)). This will give you sin^2(x) on the bottom, and a quadratic of cosines on the top.
RHS: Expand, and convert stuff until you have sin^2(x) on the bottom. This'll give you cot^(x) - csc^2(x) - 2cot(x)csc(x). Converting these to cosines and sines will give LHS.
thank you. oh my god yay.
Wow. I was JUST doing this stuff.
Lemme try now. even though its 2am.
.. nevermind.
I dun feel like finishing nymores. gosh. someone haaaad to beat me |: .
'night.
-falls on the floor- I just want to get this over with and go to sleeps @_@
:c if only i had my notes...