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Math Help - Trig - writing an equivalent expression

  1. #1
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    Trig - writing an equivalent expression

    I'm supposed to write equivalent expressions for these two expressions:

    cot(sin^-1(3x))

    and

    sin(2sin^-1(2x))

    I don't even know where to begin with these, I'm sure there's an identity I should be using to write the new expressions...but I can't figure out which one.
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  2. #2
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    Quote Originally Posted by maryanna91 View Post
    I'm supposed to write equivalent expressions for these two expressions:

    cot(sin^-1(3x))

    and

    sin(2sin^-1(2x))

    I don't even know where to begin with these, I'm sure there's an identity I should be using to write the new expressions...but I can't figure out which one.
    1) \cot \left( {{{\sin }^{ - 1}}3x} \right) = \frac{{\cos \left( {{{\sin }^{ - 1}}3x} \right)}}<br />
{{\sin \left( {{{\sin }^{ - 1}}3x} \right)}} = \frac{{\sqrt {1 - {{\left( {3x} \right)}^2}} }}<br />
{{3x}} = \frac{{\sqrt {1 - 9\,{x^2}} }}<br />
{{3x}}.

    2) \sin \left( {2{{\sin }^{ - 1}}2x} \right) = 2\sin \left( {{{\sin }^{ - 1}}2x} \right)\cos \left( {{{\sin }^{ - 1}}2x} \right) = 2 \cdot 2x\,\sqrt {1 - {{\left( {2x} \right)}^2}}  = 4x\,\sqrt {1 - 4\,{x^2}} .
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  3. #3
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    thanks a lot!
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