# sum and difference formula problems

• Dec 2nd 2009, 06:59 PM
sum and difference formula problems
can anyone do the problem cos(arccox x - arcsin x)? the problem says to write the trigonometric expression as an algebraic expression. Please show detailed steps and explain the steps if possable thanks for any help
• Dec 2nd 2009, 07:41 PM
mr fantastic
Quote:

can anyone do the problem cos(arccox x - arcsin x)? the problem says to write the trigonometric expression as an algebraic expression. Please show detailed steps and explain the steps if possable thanks for any help

Let $\arccos x = \alpha \Rightarrow \cos \alpha = x$.

Let $\arcsin x = \beta \Rightarrow \sin \beta = x$.

Find $\cos (\alpha - \beta)$ using the above together with the compound angle formula.

(The job is even easier if you realise that $\alpha + \beta = \frac{\pi}{2}$).
• Dec 2nd 2009, 08:01 PM
I just started trig so i didn't really undestand the explaination. Y does http://www.mathhelpforum.com/math-he...d83b281f-1.gif? Thanks

Also if i do open that how should i solve it?
• Dec 2nd 2009, 08:07 PM
mr fantastic
Quote:

I just started trig so i didn't really undestand the explaination. Y does http://www.mathhelpforum.com/math-he...d83b281f-1.gif? Thanks

Do it the way I said, not the clever way I mentioned in passing. Have you been taught the compound angle formulae?: Compound Angle Formulae
• Dec 2nd 2009, 08:46 PM
Yes it was covered in the chapter, if i opened it up then it would be
$
\cos \alpha \cos \beta + \sin \alpha \sin \beta$
then since $\cos \alpha = x$ and $\sin \beta = x$ i would get $x \cos \beta + x \sin \alpha$, so then i can take x out and get $x ( \cos \beta + \sin \alpha )$ i don't know w hat to do then because i don't know what $\cos \beta$ or $\sin \alpha$ equals. Thanks again
• Dec 2nd 2009, 08:51 PM
mr fantastic
Quote:

$
then since $\cos \alpha = x$ and $\sin \beta = x$ i would get $x \cos \beta + x \sin \alpha$, so then i can take x out and get $x ( \cos \beta + \sin \alpha )$ i don't know w hat to do then because i don't know what $\cos \beta$ or $\sin \alpha$ equals. Thanks again
Get $\sin \alpha$ and $\cos \beta$ using the Pythagorean identity.