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→Hyperbolic functions for complex numbers: Include tangent angle-addition formula |
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Line 375:
\cosh(ix) &= \frac{1}{2} \left(e^{i x} + e^{-i x}\right) = \cos x \\
\sinh(ix) &= \frac{1}{2} \left(e^{i x} - e^{-i x}\right) = i \sin x \\
\tanh(ix) &= i \tan x \\
\cosh(x+iy) &= \cosh(x) \cos(y) + i \sinh(x) \sin(y) \\
\sinh(x+iy) &= \sinh(x) \cos(y) + i \cosh(x) \sin(y) \\
\cosh x &= \cos(ix) \\
\sinh x &= - i \sin(ix) \\
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