Question

Решите уравнения$2sin^2x-3sin x+1=0;\tan^2x+2 ctg(pi/2+x)+1=0.$

Answer 1

2sin²x-3sinx+1=0
sinx=a
2a²-3a+1=0
D=9-8=1
a1=(3-1)/4=1/2⇒sinx=1/2⇒x=(-1)^n*π/6+πn,n∈z
a2=(3+1)/4=1⇒sinx=1⇒x=π/2+2πk,k∈z

tg²x-2tgx+1=0
(tgx-1)=0
tgx-1=0
tgx=1
x=π/4+πn,n∈z