1)8sin^2 x-6sinx-5=0
t=sinx; 8t-6t-5=0; |t|≠1
D=36-4*8*(-5)=36+160=196=14^2; t1=(6-14)/16=-8/16=-1/2 ;t2=5/4;
|t|≤0; t=5/4-посторонний
sinx=-1/2; x=(-1)^n *arcsin(-1/2)+πn; n-celoe
x=(-1)^(n+1) *π/6+πn
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2)tg^3 x=tgx
tg^3 x-tgx=0; tgx(tg^2 x -1)=0; tgx=0 ili tg^2 x -1=0
x=πn ;n-celoe tg x=-1 ili tg x=1
------------- x=-π/4+πn;x=π/4+πn
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3)(sinx+1)sinx=0
sinx+1=0 ili sinx=0
sinx=-1 x=πn
x=-π/2+2πn -----------
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4)3sin^2 x+sinx cosx =2cos^2 x-однородное уравнение
cosx≠0; 3*sin^2 x /cos^2 x)+sinx cosx /cos^2 x-2*(cos^2 x /cos^2 x)=0
3tg^2 x+tgx -2=0
tgx=t; 3t^2+t-2=0; D=1+24=25=5^2; t1=(-1-5)/6=-1; t2=(-1+5)/6=2/3
tgx=-1 ili tgx=2/3
x=-π/4+πn; n-celoe x=arctg(2/3)=πn; n-celoe
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2) -1/2cos x/7<1/4<br> cosx>-1/2; -2π/3+2πn