sum and difference formula problems

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December 2nd 2009, 06:59 PM
RexZShadow

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
December 2nd 2009, 07:41 PM
mr fantastic

Quote:

Originally Posted by RexZShadow

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 $\alpha + \beta = \frac{\pi}{2}$ ).
December 2nd 2009, 08:01 PM
RexZShadow

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?
December 2nd 2009, 08:07 PM
mr fantastic

Quote:

Originally Posted by RexZShadow

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
December 2nd 2009, 08:46 PM
RexZShadow

Yes it was covered in the chapter, if i opened it up then it would be
$<br /> \cos \alpha \cos \beta + \sin \alpha \sin \beta$ 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
December 2nd 2009, 08:51 PM
mr fantastic

Quote:

Originally Posted by RexZShadow

Yes it was covered in the chapter, if i opened it up then it would be
$<br /> \cos \alpha \cos \beta + \sin \alpha \sin \beta$ 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

Get $\sin \alpha$ and $\cos \beta$ using the Pythagorean identity.