Basic trig simplification

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December 2nd 2009, 01:44 PM
shiznid12

Basic 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.
December 2nd 2009, 01:55 PM
Jameson

Quote:

Originally Posted by shiznid12

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.

sec(y)=1/cos(y). Combine the denominator into one term, then the cancellation should be clear. If not, post your steps and we'll take a look.
December 2nd 2009, 02:01 PM
shiznid12

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.
December 2nd 2009, 02:24 PM
skeeter

Quote:

Originally Posted by shiznid12

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.

$\frac{1+\cos{y}}{1 + \sec{y}} \cdot \frac{\cos{y}}{\cos{y}} =\frac{(1+\cos{y})\cos{y}}{\cos{y} + 1} =\cos{y}$
December 2nd 2009, 02:26 PM
shiznid12

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?
December 2nd 2009, 03:18 PM
skeeter

Quote:

Originally Posted by shiznid12

Is there an explanation for why you multiply top and bottom by cos y?

experience, really ... I saw (1 + secy) in the denominator ... multiplying by cosy makes the denominator match a factor in the numerator (1 + cosy)

Better yet, why don't you multiple up the 1 + 1/cos also because it's part of the denominator too?

what would that accomplish? ... the idea here is to simplify, not make more complex.

here is probably the most basic method of simplification ...

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

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

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

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

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

...