What is the Solution for Trig Homework Question?

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The discussion revolves around solving two trigonometric equations: cot Θ + tan Θ = csc^2 Θ + sec^2 Θ and 1 - 2 cos Θ = tan Θ - cot Θ. Forum members emphasize the importance of showing work before receiving help, adhering to forum rules. They suggest using LaTeX for clarity, though it's not mandatory, and recommend rewriting equations in terms of sine and cosine for easier manipulation. The conversation highlights a collaborative approach to problem-solving, encouraging users to engage actively with their homework.
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1.)/// cot Θ + tan Θ = csc^2 Θ + sec^2 Θ
//////////////////////// -------------------
/////////////////////////// csc Θ sec Θ


2.)/// 1-2 cos Θ = tan Θ - cot Θ
////// -----------
////// sin Θ cos Θ


I also need to know how to get the solution to prove this. Thanks in advance!
:smile:
 
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1. Please do not hijack another persons thread, instead start a new one.

2. We need to see some working on your part, we don't do your homework for you.

3. What are all those slashes for? Learn LaTeX please.
 
Right.

Never mind then.
 
Whilst what Gib Z said regarding the need for you to show your work before you obtain help here is true (these are forum rules), it is not strictly necessary for you to learn LaTex. It is quite straightforward (click on the \Sigma button on the top of the reply window) but it would be sufficient for you to write equations in the forum: however, instead of using slashes to space the maths, use brackets-- e.g. (sinx+cosx)/(secx).

As for your questions, what are you doing-- proving that they are equalities? Well, I would start off by writing everything in terms of sine and cosine, then looking for possible places to cancel. If you want to have a go, then post back, we will be happy to advise.

Edit: Actually, for the first one, split the right hand side up into two fractions, and cancel-- you don't need to change into sine and cosines on this occasion.
 
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Thank you cristo.

But I'm afraid to ask again, so I think I'm going to look for help elswhere.

Peace!
 
Lol I think I scared off a member >.< my bad..
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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