Question

$arcsin( - 1) + arccos \frac{ \sqrt{2} }{2}$
$\sqrt{(2 - \sqrt{5} } ) {}^{2} + \sqrt{(3 - \sqrt{5} } ) {}^{2}$
$arcsin( \sqrt{2 - 1} ) + (1 - \sqrt{2} )$
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Answer 1

Пошаговое объяснение:

$1) \arcsin{(-1)}+\arccos{\frac{\sqrt{2} }{2} }=-\arcsin{1}+{\frac{\pi}{4} }=-{\frac{\pi}{2} }+{\frac{\pi}{4} }=-{\frac{\pi}{4} }$

$2)~ 2-\sqrt{5}<0\\2<\sqrt{5}\\\sqrt{4}<\sqrt{5}$               $3-\sqrt{5}>0\\3>\sqrt{5}\\\sqrt{9}>\sqrt{5}$

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$\sqrt{(2-\sqrt{5})^2}+\sqrt{(3-\sqrt{5})^2}=|2-\sqrt{5}|+|3-\sqrt{5}|=-(2-\sqrt{5})+(3-\sqrt{5})=\\\\=-2+\sqrt{5}+3-\sqrt{5}=1$

$3)~ \arcsin(\sqrt{2}-1)+\arcsin(1-\sqrt{2})=\arcsin(\sqrt{2}-1)+\arcsin(-(\sqrt{2}-1))=\\\\=\arcsin(\sqrt{2}-1)+(-\arcsin(\sqrt{2}-1))=\arcsin(\sqrt{2}-1)-\arcsin(\sqrt{2}-1)=0$

Answer 2

Ответ: 1) - pi/4, 2) 1, 3)1,157, см фото.

Пошаговое объяснение: