verify trig identites
- Thread starter kfox
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would the common denominator be (cos x+1)(cos x-1)? that confuses me with the top then because i thought you had to multiply the top what you do the bottom, so if i did that, it would make it (cos x+1)(cos x-1)/(cos x+1)(cos x-1), i think, and wouldn't that just all cancel out?
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- Apr 12, 2005
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How did your addition turn into multiplication?
\(\displaystyle \frac{1}{\cos(x) - 1}+\frac{1}{\cos(x) + 1} = \frac{(\cos(x) + 1) + (\cos(x) - 1)}{(\cos(x) - 1)(\cos(x) + 1)}\)
Is that better?
By the way, 1/cos(x) + 1 means \(\displaystyle \frac{1}{\cos(x)} + 1\). I'm guessing this is not what you intended. Remember your order of operations and add parentheses where necessary to enforce your intent.
\(\displaystyle \frac{1}{\cos(x) - 1}+\frac{1}{\cos(x) + 1} = \frac{(\cos(x) + 1) + (\cos(x) - 1)}{(\cos(x) - 1)(\cos(x) + 1)}\)
Is that better?
By the way, 1/cos(x) + 1 means \(\displaystyle \frac{1}{\cos(x)} + 1\). I'm guessing this is not what you intended. Remember your order of operations and add parentheses where necessary to enforce your intent.
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- Apr 12, 2005
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- 11,339
You do not seem to be understanding. I understand the problem quite nicely.kfox said:
1) Missing the "+" in the numerator is a very big deal. Please put it back and continue to simplify. You will see it. Also, multiply the two factors in the denominator. You will see somehting else.
2) There is a huge difference between "1 / (cos x +1)" and 1 / cos x + 1. It's still a little ambiguous, either way, since it's not clear if you mean "cos(x) + 1" or "cos(x+1)". The lesson, here, is not to try to justify bad notation, rather, to learn good notation.
I repeat: "Remember your order of operations and add parentheses where necessary to enforce your intent." You can't just slop it up there and have it understood.