Simple simplify question

**Ramunas** · February 1st 2009, 06:51 AM

Hello fellow mathematicians,

I've missed few classes and I ran into a big problem while doing a homework.

My question is going to be very straightforward, and I hopefully will get an answer from you soon.

Here are the two simple tasks which I'm doing
http://img140.imageshack.us/my.php?i...uestionhi0.jpg

My question is, how can I simplify these tasks.

As for 1341 excercise I want to know a way how to simplify cos 4x and sin 4x.

And as for 1349 excercise, I would like to know the answer whether there is a way to simplify sin^2x and sin^x.

I know this may sound funny, but I've forgotten how to do that and was trying all day long to figure out what I'm missing

. Thanks for a help in advance.

**running-gag** · February 1st 2009, 07:14 AM

Hi

You can use the formula

$\cos 2x = 1-2\sin^2x$

$\sin 2x = 2\sin x \cos x$

$\frac{1-cos4x}{sin4x} = \frac{1-(1-2\sin^2 2x)}{2\sin 2x \cos 2x} = \frac{\sin2x}{\cos 2x} = \tan 2x$

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