DLMF:4.21.E28 (Q1730): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
Defining formula:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2afdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1jdec

Latest revision as of 18:26, 1 January 2020

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DLMF:4.21.E28
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    Statements

    Defining formula
    cos ⁡ ( 2 ⁢ z ) = 2 ⁢ cos 2 ⁡ z - 1 = 1 - 2 ⁢ sin 2 ⁡ z = cos 2 ⁡ z - sin 2 ⁡ z = 1 - tan 2 ⁡ z 1 + tan 2 ⁡ z , 2 𝑧 2 2 𝑧 1 1 2 2 𝑧 2 𝑧 2 𝑧 1 2 𝑧 1 2 𝑧 {\displaystyle{\displaystyle\cos\left(2z\right)=2{\cos^{2}}z-1=1-2{\sin^{2}}z=% {\cos^{2}}z-{\sin^{2}}z=\frac{1-{\tan^{2}}z}{1+{\tan^{2}}z},}}
    0 references
    DLMF id
    DLMF:4.21.E28
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2asdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2ardec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2afdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1jdec
    0 references
     
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