Вложение 3,4,5,,,,,,,,,,,,,,,,. Created by kirillpolev123. algebra-ru

Вложение 3,4,5,,,,,,,,,,,,,,,,...

Artem112

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$4cos45sin135= 4\cdot\frac{ \sqrt{2} }{2} \cdot\frac{ \sqrt{2} }{2} =2
\\\
sin420cos600=sin60cos120=\frac{ \sqrt{3} }{2}\cdot(- \frac{1}{2} )=-\frac{ \sqrt{3} }{4}$
$\frac{ \sqrt{3} }{2}-sin \frac{\pi}{3} =\frac{ \sqrt{3} }{2}-\frac{ \sqrt{3} }{2}=0
\\\
sin \frac{6\pi}{5}tg \frac{7\pi}{3} =sin \frac{6\pi}{5}tg \frac{\pi}{3} = \sqrt{3} sin \frac{6\pi}{5}$
$\frac{3tg^2( \alpha +3\pi)-1}{3-tg^2( \alpha + \frac{5\pi}{2}) } =
 \frac{3tg^2 \alpha-1}{3+ctg^2 \alpha }$
$\frac{tg2 \alpha +tg3 \alpha }{1-tg2 \alpha tg3 \alpha } =tg(2 \alpha +3 \alpha )=tg5 \alpha$
$\frac{cos2 \alpha }{sin \alpha -cos \alpha } = \frac{cos^2 \alpha-sin^2 \alpha }{sin \alpha -cos \alpha } =\frac{(cos \alpha-sin \alpha )(cos \alpha+sin \alpha ) }{sin \alpha -cos \alpha } =cos \alpha-sin \alpha$
$\frac{sin3 \alpha -sin \alpha cos2 \alpha }{sin3 \alpha +sin \alpha } =
 \frac{3sin \alpha-4sin^3 \alpha -sin \alpha( cos^2 \alpha-sin^2 \alpha ) }{3sin \alpha-4sin^3 \alpha +sin \alpha } =
 \frac{3sin \alpha-3sin^3 \alpha -sin \alpha cos^2 \alpha }{4sin \alpha-4sin^3 \alpha } =
\\\
 \frac{3-3sin^2 \alpha -cos^2 \alpha }{4-4sin^2 \alpha }$
$cos^4 \frac{ \alpha }{4} -sin^4 \frac{ \alpha }{4} -cos \alpha =
cos^2 \frac{ \alpha }{2} -cos \alpha =
 \frac{1+cos \alpha-2cos \alpha }{2} = \frac{1-cos \alpha }{2}$
$cos^4 \alpha (1+tg^2 \alpha )+sin^2 \alpha =
 \frac{cos^4 \alpha }{cos^2 \alpha } +sin^2 \alpha =cos^2 \alpha +sin^2 \alpha =1$

$sin138>0
\\\
cos50>0
\\\
sin138+cos50>0$

$sin \frac{2\pi}{3} - \frac{ \sqrt{3} }{2} = \frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2} =0$

$sin \frac{7\pi}{5}
\\\
sin \frac{17\pi}{10}=sin \frac{8.5\pi}{5}
\\\
sin \frac{7\pi}{5}-sin \frac{17\pi}{10}$

$3.14$

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