485 - 2 и 4 486 - 2 487 - 2 и 4. Created by Akula17. geometriya-ru

485 - 2 и 4 486 - 2 487

Akula17 @Akula17

October 2021 1 24 Report

485 - 2 и 4
486 - 2
487 - 2 и 4

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Artem112

Verified answer

485
$\sin73\cos13-\cos73\sin13=\sin(73-13)=\sin60= \frac{ \sqrt{3} }{2} 
\\\
\sin \frac{7 \pi }{12} \cos \frac{\pi }{12}-\sin \frac{ \pi }{12} \cos \frac{7\pi }{12}=\sin( \frac{7 \pi }{12} -\cos \frac{\pi }{12})=\sin \frac{6 \pi }{12} =1$

486
Так как угол принадлежит 2 четверти, то его косинус отрицателен
$\cos \alpha =- \sqrt{1-\sin^2 \alpha } =-\sqrt{1-( \frac{ \sqrt{2} }{3})^2 } =-\sqrt{\frac{ 7 }{9} } =- \frac{ \sqrt{7} }{3}$
$\sin( \frac{ \pi }{4} - \alpha )=\sin \frac{ \pi }{4} \cos \alpha -\sin \alpha \cos \frac{ \pi }{4} =
\frac{ \sqrt{2} }{2}\cdot(- \frac{ \sqrt{7} }{3} ) - \frac{ \sqrt{2} }{ 3 }\cdot\frac{ \sqrt{2} }{2}=
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=-\frac{ \sqrt{14} }{6}-\frac{2 }{6}=- \frac{2 + \sqrt{14} }{6}$

487
$\cos(- \alpha )\sin(- \beta )-\sin( \alpha - \beta )=
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=-\cos \alpha \sin \beta -(\sin \alpha \cos\beta-\cos \alpha \sin \beta )=
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=-\cos \alpha \sin \beta -\sin \alpha \cos\beta+\cos \alpha \sin \beta =-\sin \alpha \cos\beta
\\\
$
$\sin( \alpha + \beta )+\sin( \frac{ \pi }{2} - \alpha )\sin(- \beta )=
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=\sin \alpha \cos \beta +\cos \alpha \sin \beta -\cos \alpha \sin \beta =
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=\sin \alpha \cos \beta +\cos \alpha \sin \beta -\cos \alpha \sin \beta =\sin \alpha \cos \beta$

30112000 спс

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