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June 14th, 2010, 06:49 PM   #1
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[TRIG] Indentities

I need help with some unlisted identities.

Like for example:
(secx) (secx) = sec^2x = 2secx ??
(cscx - 1) (cscx + 1) = ?
(1 - cosx) - (1 + cosx) = ?
(secx + tanx) + (secx - tanx) = ?
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June 14th, 2010, 07:11 PM   #2
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They seem straightforward; can you explain why they are troubling you?
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June 14th, 2010, 07:22 PM   #3
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Re: [TRIG] Indentities

I just don't understand what to do when I come into those situations.

Like I don't understand how/why (cscx-1) (cscx+1) = (1/sinx) - (1/1)
And the others listed in 1st post.
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June 15th, 2010, 02:01 AM   #4
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Re: [TRIG] Indentities

Quote:
Originally Posted by RMG46
I just don't understand what to do when I come into those situations.

Like I don't understand how/why (cscx-1) (cscx+1) = (1/sinx) - (1/1)
And the others listed in 1st post.
That identity doesn't hold. Substitute any value of x to test it.
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June 15th, 2010, 04:20 AM   #5
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Re: [TRIG] Indentities

So what I'm asking is what does it equal then?
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June 15th, 2010, 06:02 AM   #6
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You need to find the total of the (four in this case) products of each term within the first pair of parentheses and each term within the second pair of parentheses:

(csc(x) - 1)(csc(x) + 1) = csc²(x) + csc(x) - csc(x) - 1 = csc²(x) - 1.

The result simplifies further to cot²(x), since there is a standard identity (corresponding to Pythagoras) that tells you that cot²(x) + 1 = csc²(x).

The last two of your original examples didn't involve multiplication; you just needed to be able to add and subtract. Why were those causing difficulty for you? Are you perhaps tackling trigonometry without taking the trouble to revise the basics of arithmetic, algebra and geometry first?
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June 15th, 2010, 06:16 AM   #7
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Re: [TRIG] Indentities

Doesn't the Pythagorean Theorem state: 1 + cot²x = csc²x
Not: cot²x - 1 = csc²x
Or is it the same thing?
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June 15th, 2010, 06:31 AM   #8
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Re: [TRIG] Indentities

And like what do these equal to:

csc²x = ?
cot²x = ?
sec²x = ?
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June 15th, 2010, 08:09 AM   #9
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Quote:
Originally Posted by RMG46
Doesn't the Pythagorean Theorem state: 1 + cot²x = csc²x
Yes, but the order of the terms in the left-hand side doesn't matter.
Quote:
Originally Posted by RMG46
Not: cot²x - 1 = csc²x
Correct again; that's not the same thing, not an identity, and not what I posted!

Quote:
Originally Posted by RMG46
csc²x = ?
cot²x = ?
sec²x = ?
They are already simplified. How complicated would you want to make them?
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