DLMF:4.24.E16 (Q1810)

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DLMF:4.24.E16
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    Statements

    test
    Arcsin ⁡ u ± Arccos ⁡ v = Arcsin ⁡ ( u ⁢ v ± ( ( 1 - u 2 ) ⁢ ( 1 - v 2 ) ) 1 / 2 ) = Arccos ⁡ ( v ⁢ ( 1 - u 2 ) 1 / 2 ∓ u ⁢ ( 1 - v 2 ) 1 / 2 ) , plus-or-minus multivalued-inverse-sine 𝑢 multivalued-inverse-cosine 𝑣 multivalued-inverse-sine plus-or-minus 𝑢 𝑣 superscript 1 superscript 𝑢 2 1 superscript 𝑣 2 1 2 multivalued-inverse-cosine minus-or-plus 𝑣 superscript 1 superscript 𝑢 2 1 2 𝑢 superscript 1 superscript 𝑣 2 1 2 {\displaystyle{\displaystyle\operatorname{Arcsin}u\pm\operatorname{Arccos}v=% \operatorname{Arcsin}\left(uv\pm((1-u^{2})(1-v^{2}))^{1/2}\right)=% \operatorname{Arccos}\left(v(1-u^{2})^{1/2}\mp u(1-v^{2})^{1/2}\right),}}
    0 references
    DLMF id
    DLMF:4.24.E16
    0 references
    Symbols used
    general arccosine function
    test
    Arccos ⁡ z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}
    xml-id
    C4.S23.E2.m2aadec
    0 references
    general arcsine function
    test
    Arcsin ⁡ z multivalued-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsin}\NVar{z}}}
    xml-id
    C4.S23.E1.m2aadec
    0 references
     
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