вычислите: arctg√2-arctg(1/√2). Created by Hatug. algebra-ru

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Hatug @Hatug

October 2021 1 6 Report

вычислите: arctg√2-arctg(1/√2)

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dnepr1

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Это задание можно выполнить двумя способами.
1) arctg√2 = 0,955317 радиан = 54,73561°,
arctg(1/√2) = 0,61548 радиан = 35,26439°.
arctg√2-arctg(1/√2) = 54,73561° - 35,26439° = 19,47122°.

2) Возьмём тангенс заданной разности углов.
$tg( \alpha - \beta )= \frac{tg \alpha -tg \beta }{1+tg \alpha *tg \beta }= \frac{ \sqrt{2}- \frac{1}{ \sqrt{2} } }{1+ \sqrt{2}* \frac{1}{ \sqrt{2} } } = \frac{1}{2 \sqrt{2} }$ .
$arctg( \frac{1}{2 \sqrt{2} })=$ 0,339837 радиан = 19,47122°.

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