DLMF:19.8#Ex7 (Q6220)

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DLMF:19.8#Ex7
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    ϕ 1 = ϕ + arctan ( k tan ϕ ) = arcsin ( ( 1 + k ) sin ϕ cos ϕ 1 - k 2 sin 2 ϕ ) . subscript italic-ϕ 1 italic-ϕ superscript 𝑘 italic-ϕ 1 superscript 𝑘 italic-ϕ italic-ϕ 1 superscript 𝑘 2 2 italic-ϕ {\displaystyle{\displaystyle\phi_{1}=\phi+\operatorname{arctan}\left(k^{\prime% }\tan\phi\right)=\operatorname{arcsin}\left((1+k^{\prime})\frac{\sin\phi\cos% \phi}{\sqrt{1-k^{2}{\sin^{2}}\phi}}\right).}}
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    DLMF:19.8#Ex7
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