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 $\displaystyle \arccos x = \alpha \Rightarrow \cos \alpha = x$.
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 $\displaystyle \alpha + \beta = \frac{\pi}{2}$).
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
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