I am having the HARDEST TIME simplifying this into cos y

(1+cos y)/(1+sec y)

When I do it, I always end up with cos^2 y..

Thanks guys, appreciate it.

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- Dec 2nd 2009, 01:44 PMshiznid12Basic trig simplification
I am having the HARDEST TIME simplifying this into cos y

(1+cos y)/(1+sec y)

When I do it, I always end up with cos^2 y..

Thanks guys, appreciate it. - Dec 2nd 2009, 01:55 PMJameson
- Dec 2nd 2009, 02:01 PMshiznid12
I understand that... but how would it cancel out

(1+cos y)/(1+1/cos y)

I understand the 1's would/could cancel, but then you still have:

cos y/(1/cos y)

And the only way I can imagine you would get rid of the denom is multiply the cos y uptop.

I'm clearly doing something wrong, and this is the only problem i've had any issues with thus far. - Dec 2nd 2009, 02:24 PMskeeter
- Dec 2nd 2009, 02:26 PMshiznid12
Is there an explanation for why you multiply top and bottom by cos y?

That would be very useful knowledge for my test tomorrow.

:)

Better yet, why don't you multiple up the 1 + 1/cos also because it's part of the denominator too? - Dec 2nd 2009, 03:18 PMskeeter
here is probably the most basic method of simplification ...

$\displaystyle \frac{1+\cos{y}}{1+\sec{y}} = $

$\displaystyle \frac{1+\cos{y}}{1 + \frac{1}{\cos{y}}} =$

$\displaystyle \frac{1+\cos{y}}{\frac{\cos{y}}{\cos{y}} + \frac{1}{\cos{y}}} =$

$\displaystyle \frac{1+\cos{y}}{\frac{\cos{y}+1}{\cos{y}}} =$

$\displaystyle \frac{1+\cos{y}}{1} \cdot \frac{\cos{y}}{\cos{y}+1} = \cos{y}$

...