sum and difference formula problems

**RexZShadow** · December 2nd 2009, 06:59 PM

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

**mr fantastic** · December 2nd 2009, 07:41 PM

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 $\alpha + \beta = \frac{\pi}{2}$ ).

**RexZShadow** · December 2nd 2009, 08:01 PM

I just started trig so i didn't really undestand the explaination. Y does

? Thanks

Also if i do open that how should i solve it?

**mr fantastic** · December 2nd 2009, 08:07 PM

Originally Posted by RexZShadow

I just started trig so i didn't really undestand the explaination. Y does

? 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

**RexZShadow** · December 2nd 2009, 08:46 PM

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

**mr fantastic** · December 2nd 2009, 08:51 PM

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.

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