1) 2sinП/8*cosП/8 2)sinП/8*cosП/8+1/4 3)cos^2*П/8-sin^2*П/8 4)корень из 2/2-(cosП/8+sinП/8)^2. Created by Allinochka. algebra-ru

1) 2sinП/8*cosП/8 - это формула двойного угла 2) 3) cos^2*П/8-sin^2*П/8 - это формула двойного угла 4)

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Allinochka @Allinochka

August 2021 1 37 Report

1) 2sinП/8*cosП/8

2)sinП/8*cosП/8+1/4

3)cos^2*П/8-sin^2*П/8

4)корень из 2/2-(cosП/8+sinП/8)^2

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fou

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1) 2sinП/8*cosП/8 - это формула двойного угла

$2sin\frac{\pi}{8}cos\frac{\pi}{8} = sin\frac{\pi}{4} = \frac{\sqrt{2}}{2}$

2) $sin\frac{\pi}{8}cos\frac{\pi}{8} + \frac{1}{4}= \frac{sin\frac{\pi}{4}}{2}+ \frac{1}{4} = \frac{\sqrt{2}+1}{4}$

3) cos^2*П/8-sin^2*П/8 - это формула двойного угла

$sin^{2}\frac{\pi}{8}-cos^{2}\frac{\pi}{8} = cos\frac{\pi}{4} = \frac{\sqrt{2}}{2}$

4) $\frac{\sqrt{2}}{2} - (sin\frac{\pi}{8}+cos\frac{\pi}{8})^{2}= \frac{\sqrt{2}}{2} - (sin^{2}\frac{\pi}{8}+cos^{2}\frac{\pi}{8}+2sin\frac{\pi}{8}cos\frac{\pi}{8})=\\= \frac{\sqrt{2}}{2} -(1+sin\frac{\pi}{4}) =\frac{\sqrt{2}}{2}-1-\frac{\sqrt{2}}{2}=-1$

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