cos-pi-2-1-2-arccos-4-5-

Question Number 149408 by mathdanisur last updated on 05/Aug/21

c o s (\frac{π}{2} - \frac{1}{2} a r c c o s \frac{4}{5}) = ?

Commented by liberty last updated on 05/Aug/21

\sin (\frac{1}{2} \arccos \frac{4}{5}) = \sin u

\frac{1}{2} \arccos \frac{4}{5} = u \Rightarrow \arccos \frac{4}{5} = 2 u

\cos 2 u = \frac{4}{5} \Rightarrow 1 - 2 \sin^{2} u = \frac{4}{5}

\sin u = \sqrt{\frac{1}{10}} = \frac{1}{\sqrt{10}}

Commented by mathdanisur last updated on 05/Aug/21

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