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Math Help - sum and difference formula problems

  1. #1
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    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
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    Quote Originally Posted by RexZShadow View Post
    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}).
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    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?
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    Quote Originally Posted by RexZShadow View Post
    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
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  5. #5
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    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
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  6. #6
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    Quote Originally Posted by RexZShadow View Post
    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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