# Need help with trig identities problem

Discussion in 'Homework Help' started by strantor, Feb 27, 2013.

1. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
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PLZ NEED HLP URGENT.

I kid, I kid. I had this question in my homework last week and tried probably 5 times and then wrote it off as a loss. Now it's come back around to abuse me on a take home quiz. So I've just now tried it another 7 or 8 times and about to pull my hair out. I'm supposed to pick either the left side or the right side, and using trig identities, work through the problem until the 2 sides are the same. I've tried both side and gotten nowhere.

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2. ### MrChips Moderator

Oct 2, 2009
17,548
5,449
Your first line is ok.
Don't expand the denominator.
Expand the nominator, as you have done on the second line.
Your result of 2 + 2sin is correct.
The identity should be obvious from there.

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3. ### MrChips Moderator

Oct 2, 2009
17,548
5,449
Note that this identity is not true under two conditions.

4. ### amilton542 Active Member

Nov 13, 2010
496
64
$\frac{cos(x)}{1 + sin(x)} + \frac{1 + sin(x)}{cos{x}} =$

$\frac{cos^2(x) + [1 + sin(x)]^2}{[cos(x)][1 + sin(x)]} =$

$\frac{[cos^2(x) + sin^2(x)] + [1 + 2sin(x)]}{[cos(x)][1 + sin(x)]} =$

$\frac{2 + 2sin(x)}{[cos(x)][1 + sin(x)]} =$

$\frac{(2)(1 + sin(x))}{[cos(x)][1 + sin(x)]} = 2sec(x)$

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5. ### strantor Thread Starter AAC Fanatic!

Oct 3, 2010
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3,060
DOH! So simple. Thank you MrChips!

Edit: and amilton too!

6. ### amilton542 Active Member

Nov 13, 2010
496
64
${f:x \rightarrow 2sec(x) x\epsilon R\ x \neq (2n + 1) 90^{o} n \epsilon Z}$