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.
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.
here is probably the most basic method of simplification ...
$\displaystyle \frac{1+\cos{y}}{1+\sec{y}} = $
$\displaystyle \frac{1+\cos{y}}{1 + \frac{1}{\cos{y}}} =$
$\displaystyle \frac{1+\cos{y}}{\frac{\cos{y}}{\cos{y}} + \frac{1}{\cos{y}}} =$
$\displaystyle \frac{1+\cos{y}}{\frac{\cos{y}+1}{\cos{y}}} =$
$\displaystyle \frac{1+\cos{y}}{1} \cdot \frac{\cos{y}}{\cos{y}+1} = \cos{y}$
...