I have been teaching myself calculus and in the process came across this equation:- 1/2*sin x/2*cos x/2. Can somebody show me how to simplify it? I am sure it involves the identity sin 2x=2*sin x*cos x.

Printable View

- Jan 17th 2010, 12:34 AMp75213Simplify
I have been teaching myself calculus and in the process came across this equation:- 1/2*sin x/2*cos x/2. Can somebody show me how to simplify it? I am sure it involves the identity sin 2x=2*sin x*cos x.

- Jan 17th 2010, 01:00 AMProve It
Are you asking to simplify

$\displaystyle \frac{1}{2}\sin{\frac{x}{2}}\cos{\frac{x}{2}}$?

Yes, you do use the identity $\displaystyle \sin{2\theta} = 2\sin{\theta}\cos{\theta}$.

If you let $\displaystyle \theta = \frac{x}{2}$

we have $\displaystyle \frac{1}{2}\sin{\theta}\cos{\theta}$

$\displaystyle = \frac{1}{4}\cdot 2\sin{\theta}\cos{\theta}$

$\displaystyle = \frac{1}{4}\sin{2\theta}$

$\displaystyle = \frac{1}{4}\sin{\frac{2x}{2}}$

$\displaystyle = \frac{1}{4}\sin{x}$. - Jan 17th 2010, 01:24 AMp75213Many Thanks for the quick response.
I won't tell you how long I stuffed around with this. Tricky little bugger - but not so difficult when somebody shows you how. Text books that just give you the answer without showing you how it was arrived at drive me nuts.

- Jan 17th 2010, 05:03 PMProve It
Can you buy a solutions book that goes with your text book?

- Jan 17th 2010, 07:09 PMp75213
The solutions are given but sometimes the workings are very brief (important chunks missed out). In most cases I have been able to figure it out with the help of google. However it would be a time saver if everything was in the answer given without having to go searching on the internet.