2=1,5+sin x 3. tg(x-15°)ctg(x+15°)=⅓...

June 2022 1 12 Report

1. а) sin(x-1)=cos(x+2)
б) sin(3x+3)=cos(x-1)
2. а)8sin² x/2-3sin x-4=0 б)4sin² x/2-cos² x/2=1,5+sin x
3. tg(x-15°)ctg(x+15°)=⅓

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DHAcity $1)$
$a)sin(x-1)=cos(x+2)$
$cos( \frac{ \pi }{2} -x+1)=cos(x+2)$
$\frac{ \pi }{2} -x+1=x+2+2 \pi k$
$-2x=1- \frac{ \pi }{2} +2 \pi k$
$x= \frac{1}{2} ( \frac{ \pi }{2} -1+2 \pi k)$

$b)sin(3x+3)=cos(x-1)$
$sin(3x+3)=sin( \frac{ \pi }{2} -(x-1))$
$3x+3=\frac{ \pi }{2} -(x-1)+2 \pi k и 3x+3= \frac{ \pi }{2} +(x-1)+2 \pi k, kZ.$
$x=\frac{( \frac{ \pi }{2} -2+2 \pi k)}{y}$
$x= \frac{( \frac{ \pi }{2} -4+2 \pi k)}{2} = \frac{ \pi }{4-2+ \pi k}$
$x= \frac{( \frac{ \pi }{2} -2+2 \pi k)}{4}$
$\frac{ x= \pi }{4-2+ \pi k} , kZ$

$2)$
$a)8sin^2 x/2-6sin(x/2)cjs(x/2)-4(sin^2(x/2)+cos^2(x/2))=0$
$4sin^2(x/2)-6sinx/2cosx/2-4cjs^2(x/2)=0$
$4tg^2x/2-6tgx/2-4=0$
$y=tgx/2$
$4y^2-6y-4=0 2y^2-3y-2=0 y=2y=-0,5 tgx/2=2$
$x/2=arctg2+ \pi k;$
$x=2arctg2+2 \pi k$
$tgx/2=-0,5$
$x=2arctg0,5+ \pi k$

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a1 chem pomestnoe zemlevladenie otlichalos ot votchiny 1 posle smerti vladelca

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