tex]...

масяня3009 @масяня3009

July 2022 1 13 Report

[tex]1. sin(x + \frac{2\pi}{3} ) * sin(x - \frac{\pi}{3})
2. sin(x + \frac{\pi}{4} ) * sin(x - \frac{\pi}{3}) [/tex]

Answers & Comments

Artem112

Verified answer

$sin(x + \frac{2\pi}{3} ) sin(x - \frac{\pi}{3}) = \\\ =0,5(cos(x + \frac{2\pi}{3}-x+ \frac{\pi}{3})-cos(x + \frac{2\pi}{3}+x - \frac{\pi}{3}))=
\\\ =0,5(cos\pi-cos(2x + \frac{\pi}{3} ))=-0.5-0.5cos(2x + \frac{\pi}{3} )$

$sin(x + \frac{\pi}{4} ) sin(x - \frac{\pi}{3}) = \\\ =0,5(cos(x + \frac{\pi}{4}-x+ \frac{\pi}{3})-cos(x + \frac{\pi}{4}+x - \frac{\pi}{3}))=
\\\ =0,5(cos \frac{7\pi}{12}-cos(2x- \frac{\pi}{12}))=
0,5cos \frac{7\pi}{12}-0.5cos(2x- \frac{\pi}{12})$

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