what is (1 over cos theta sin theta)cos theta in terms of sin theta?

Question

anonymous · Answer

Is this how it looks?
$$\frac{ 1 }{ \cos \Theta \sin \Theta }\sin \Theta$$

anonymous · Answer

yes :D

anonymous · Answer

okay perfect! think about what can you cancel now?

anonymous · Answer

ahh my bad wait a sec

anonymous · Answer

$$\frac{ 1 }{ \cos \Theta \sin \Theta } \cos \Theta $$

anonymous · Answer

okay now think what you can cancel?

anonymous · Answer

the cos theta?

anonymous · Answer

yup!
so what do you get?

anonymous · Answer

(1/sin theta)cos theta

anonymous · Answer

is that really it? thats all...?

anonymous · Answer

once you cancel the cos theta, there's no cos theta left

anonymous · Answer

you're only left with sin theta

anonymous · Answer

right?

anonymous · Answer

yeah, X) thanks so much!

anonymous · Answer

:)

anonymous · Answer

Just a friendly reminder.  The sin theta is in the denominator of the fraction, so 1 over sine theta is equivalent to cosecant theta, or $$\frac{ 1 }{\sin \Theta }=\csc \Theta $$

anonymous · Answer

right the ques however only asked in terms of sin

anonymous · Answer

oops, well, as long as he/she left it in the denominator.  Many students tend to write the answer without the 1 on top.