DLMF:4.21.E39 (Q1743)

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DLMF:4.21.E39
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    tan z = sin ( 2 x ) + i sinh ( 2 y ) cos ( 2 x ) + cosh ( 2 y ) , 𝑧 2 𝑥 imaginary-unit 2 𝑦 2 𝑥 2 𝑦 {\displaystyle{\displaystyle\tan z=\frac{\sin\left(2x\right)+\mathrm{i}\sinh% \left(2y\right)}{\cos\left(2x\right)+\cosh\left(2y\right)},}}
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    DLMF:4.21.E39
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    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aaadec
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    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2abdec
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    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2abdec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2azdec
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    tan z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    C4.S14.E4.m2ahdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C4.S1.XMD6.m1bdec
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    y 𝑦 {\displaystyle{\displaystyle y}}
    C4.S1.XMD7.m1bdec
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