tex]...

July 2022 1 12 Report

Нужно решить Cos([tex] \frac{ \pi }{2} -arcsin \frac{1}{3} )[/tex]

и уравнение: arcsin(3-x-2)=[tex] \frac{ \pi }{2} [/tex]

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bearcab

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1) По формуле косинуса разности
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
$\cos(\frac{\pi}{2}-\arcsin\frac{1}{3})=\cos\frac{\pi}{2}\cos(\arcsin\frac{1}{3})-\sin\frac{\pi}{2}\sin(\arcsin\frac{1}{3})=$

$=0*\cos(\arcsin\frac{1}{3})-1*\sin(\arcsin\frac{1}{3})=-\sin(\arcsin\frac{1}{3})=-\frac{1}{3}$

2) $\arcsin(3-x-2)=\frac{\pi}{2}$

$\arcsin(1-x)=\frac{\pi}{2}$

$(1-x)=\sin\frac{\pi}{2}$

$1-x=1$

$x=1-1$

x=0

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