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Tangent half-angle formula : ウィキペディア英語版
Tangent half-angle formula

In trigonometry, the tangent half-angle formulas relate the tangent of one half of an angle to trigonometric functions of the entire angle. They are as follows:
:\sin \alpha = \frac}}
:\cos \alpha = \frac}}
:\tan \alpha = \frac}}
There are also a number of different forms:
:
\begin
\tan\left(\frac \right) & = \frac = -\frac, \\()
\tan\left(\pm\frac\right) & = \frac = \frac = \frac, ~~~~(\eta = 0) \\()
\tan\left(\pm\frac\right) & = \frac = \frac = \pm(\csc\theta-\cot\theta), ~~~~(\eta=0) \\()
\tan\left(\frac \pm \frac \right) & = \frac = \sec\theta \pm \tan\theta = \frac, ~~~~(\eta=\frac) \\()
\tan\left(\frac \pm \frac \right) & = \frac = \frac = \frac, ~~~~(\eta=\frac) \\()
\frac & = \sqrt}.
\end

==Proofs==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Tangent half-angle formula」の詳細全文を読む



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