Предмет: Алгебра, автор: Владимир2015

а)2sin^x-5sinx-3=0
б) 2tg+2ctg=5

Ответы

Автор ответа: sedinalana

2sin²x-5sinx-3=0
sinx=a
2a²-5a-3=0
D=25+24=49
a1=(5-7)/4=-1/2⇒sinx=-1/2⇒x=(-1)^(n+1)*π/6+πn,n∈z
a2=(5+7)/4=3⇒sinx=3>1 нет решения

2tgx+2ctgx=5
2tgx+2/tgx-5=0
2tg²x-5tgx+2=0,tgx≠0
tgx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=0,5⇒tgx=0,5⇒x=arctg0,5+πn,n∈z
a2=(5+3)/4=2⇒tgx=2⇒x=arctg2+πk,k∈z

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