HPlourde Group Title what is (cosx/sinx)/sinxcosx simplified one year ago one year ago

1. abb0t Group Title

$\frac{ \cos(x) }{ \sin(x) } \times \frac{ \sin(x)\cos(x) }{ 1 }$

2. zepdrix Group Title

$\large \frac{\left(\dfrac{\cos x}{\sin x}\right)}{\sin x \cos x}$Woops I dunno if you're looking at it correctly abbot :O Only the top one is a fraction.

3. zepdrix Group Title

$\large \frac{\left(\dfrac{\cos x}{\sin x}\right)}{\sin x \cos x} \qquad = \qquad \left(\frac{\cos x}{\sin x}\right)\frac{1}{\sin x \cos x}$

4. HPlourde Group Title

ya but what about multiplying by the recipricol.... cause i am seriously confused.

5. zepdrix Group Title

$\large \left(\frac{\cancel{\cos x}}{\sin x}\right)\frac{1}{\sin x \cancel{\cos x}}$

6. zepdrix Group Title

Ok here's the thing with the reciprocal :) lemme explain.

7. HPlourde Group Title

ok sounds good

8. zepdrix Group Title

The bottom fraction is actually this,$\large \frac{\sin x \cos x}{1}$ So if you wanted to write it as a division of fractions, you could write it like this,$\large \frac{\left(\dfrac{\cos x}{\sin x}\right)}{\sin x \cos x} \qquad = \qquad \frac{\left(\dfrac{\cos x}{\sin x}\right)}{\left(\dfrac{\sin x \cos x}{1}\right)}$And then from here, we could multiply by the reciprocal of the bottom fraction.

9. HPlourde Group Title

aha!!!!! now it's making sense!!!

10. zepdrix Group Title

When we started this problem, we weren't dividing fractions. Only the top one was a fraction. Maybe that's why there was a little confusion :)

11. HPlourde Group Title

i think so...this is the only one that i've been confused over so far... thank you:)

12. HPlourde Group Title

i got the right answer. thanks a billion

13. zepdrix Group Title

yay!