1. Quick question

Can someone explain to me how you can go from
$\displaystyle (\frac{cosx+sinx}{cosx})(\frac{cosx}{1})$
to
$\displaystyle =cosx+sinx$

I thought it would be (sinx)(cosx), so I must not understand something!

Thanks!

2. Re: Quick question

Originally Posted by whit221
Can someone explain to me how you can go from
$\displaystyle (\frac{cosx+sinx}{cosx})(\frac{cosx}{1})$
to
$\displaystyle =cosx+sinx$

I thought it would be (sinx)(cosx), so I must not understand something!

Thanks!
Do you see that $\displaystyle (\frac{a+b}{c})(\frac{c}{1})=a+b~?$

3. Re: Quick question

I don't see how you could possibly think that canceling the cos(x) in both numerator and denominator will cause "cos(x) plus sin(x)" to become "cos(x) times sin(x)".

4. Re: Quick question

Hello, whit221!

Can someone explain to me how you can go
. . from $\displaystyle \frac{\cos x+\sin x}{\cos x}\cdot\frac{\cos x}{1}$ to $\displaystyle \cos x+\sin x$

I thought it would be $\displaystyle \sin x\cos x$

Did you do something really silly?

. . $\displaystyle \frac{{\color{red}\rlap{////}}\cos x + \sin x}{{\color{red}\rlap{////}}{\cos x}}\cdot \dfrac{\cos x}{1} \;=\;\sin x\cos x$