Разделим на cos²x
5tg²x-3tgx-2=0
tgx=a
5a²-3a-2=0
D=9+40=49
a1=(3-7)/10=-0,4⇒tgx=-0,4⇒x=-arctg0,4+πn,n∈z
a2=(3+7)/10=1⇒tgx=1⇒x=π/4+πn,n∈z
p - пи
э - принадлежит
\э\ - не принадлежит
sin x - cos x - sin x * cos x = 1
sin x (1 - cos x - cos x) = 1
sin x = 1
x = p/2<span> +2p n, n э Z</span>
<span>n = 0</span>
<span> x = <span>p/2 , э [ -p ;p ];</span></span>
<span><span>n = 1</span></span>
<span><span>x = p/2 + 2p </span></span>, \э\ [-p ;p ];
n = 2
x = p/2 + 4p, \э\ [-p;p];
n = -1
x = p/2 - 2p, \э\ [-p;p];
n = -2
x = p/2 - 4p, \э\ [-p;p];
Ответ: x = p/2+2p n, n э Z; x = p/2;