# Thread: sum and difference formula problems

1. ## 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

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

3. 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?

4. 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

5. 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

6. Originally Posted by RexZShadow
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
Get $\sin \alpha$ and $\cos \beta$ using the Pythagorean identity.