Math Is Fun Forum

24680

Member

Registered: 2007-02-01

Posts: 1

trig proofing. very smart person needed

Hello,
I am currently trying to make a difficult trig proof for my maths lesson. If someone could help me make one, that would be very helpful. I have been given a left hand side, ((cosec(x))^2)\(2+cot(x)). I need it to be changed into something as different as possible from the original, with as many difficult steps as possible, without a very long right hand side. Feel free to use all trig rules.
If someone could do this for me it would be great.
Thanks in advance,
James

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: trig proofing. very smart person needed

That's a bit of a strange task. Normally you'd just want to make it as simple as possible.

One identity that will probably help you is that cosec² x = 1 + cot² x. Using that will help you get everything in terms of cot.

After that, there are lots of things you could do. You'll have a fraction where the numerator is of higher order than the denominator, so you could try algebraic division on it if you wanted.

Or maybe you could use a few more identities to turn the cots into different functions, to make it look more different. There are tons of things you could do.

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246800

Guest

Re: trig proofing. very smart person needed

I basically need a trig proof out of ((cosec(x))^2)\(2+cot(x)) so ((cosec(x))^2)\(2+cot(x)) = ..... but it needs to be as complex and compact as possible with lots of steps involved. Thankyou for replies so far.

246800

Guest

Re: trig proofing. very smart person needed

Yeh basically, but I want it to be as difficult as possible to get to.
Cheers,
James

krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: trig proofing. very smart person needed

you're searching for:

You can use:

and:

to get formula only with sin and cos

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: trig proofing. very smart person needed

Here's a plot:

Last edited by krassi_holmz (2007-02-03 22:12:36)

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246800

Guest

Re: trig proofing. very smart person needed

many thanks. that i.z thing seems pretty good. cheers