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

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- Dec 2nd 2009, 06:59 PMRexZShadowsum 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 PMmr fantastic
Let $\displaystyle \arccos x = \alpha \Rightarrow \cos \alpha = x$.

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

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

(The job is even easier if you realise that $\displaystyle \alpha + \beta = \frac{\pi}{2}$). - Dec 2nd 2009, 08:01 PMRexZShadow
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 PMmr fantastic
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 PMRexZShadow
Yes it was covered in the chapter, if i opened it up then it would be

$\displaystyle

\cos \alpha \cos \beta + \sin \alpha \sin \beta $ then since $\displaystyle \cos \alpha = x $ and $\displaystyle \sin \beta = x $ i would get $\displaystyle x \cos \beta + x \sin \alpha $, so then i can take x out and get $\displaystyle x ( \cos \beta + \sin \alpha ) $ i don't know w hat to do then because i don't know what $\displaystyle \cos \beta $ or $\displaystyle \sin \alpha $ equals. Thanks again - Dec 2nd 2009, 08:51 PMmr fantastic