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

[latex]1)[/latex] [latex]a)sin(x-1)=cos(x+2)[/latex] [latex]cos( \frac{ \pi }{2} -x+1)=cos(x+2) [/latex] [latex] \frac{ \pi }{2} -x+1=x+2+2 \pi k [/latex] [latex]-2x=1- \frac{ \pi }{2} +2 \pi k [/latex] [latex]x= \frac{1}{2} ( \frac{ \pi }{2} -1+2 \pi k)[/latex] [latex]b)sin(3x+3)=cos(x-1)[/latex] [latex]sin(3x+3)=sin( \frac{ \pi }{2} -(x-1))[/latex] [latex]3x+3=\frac{ \pi }{2} -(x-1)+2 \pi k и 3x+3= \frac{ \pi }{2} +(x-1)+2 \pi k, kZ.[/latex] [latex]x=\frac{( \frac{ \pi }{2} -2+2 \pi k)}{y} [/latex] [latex]x= \frac{( \frac{ \pi }{2} -4+2 \pi k)}{2} = \frac{ \pi }{4-2+ \pi k} [/latex] [latex]x= \frac{( \frac{ \pi }{2} -2+2 \pi k)}{4} [/latex] [latex]\frac{ x= \pi }{4-2+ \pi k} , kZ[/latex] [latex]2)[/latex] [latex]a)8sin^2 x/2-6sin(x/2)cjs(x/2)-4(sin^2(x/2)+cos^2(x/2))=0 [/latex] [latex]4sin^2(x/2)-6sinx/2cosx/2-4cjs^2(x/2)=0[/latex] [latex]4tg^2x/2-6tgx/2-4=0 [/latex] [latex]y=tgx/2[/latex]       [latex]4y^2-6y-4=0 2y^2-3y-2=0 y=2y=-0,5 tgx/2=2 [/latex] [latex]x/2=arctg2+ \pi k; [/latex] [latex] x=2arctg2+2 \pi k [/latex] [latex] tgx/2=-0,5 [/latex] [latex]x=2arctg0,5+ \pi k[/latex]