Question

Решите уравнение:3sinx+1=cos2x

Answer 1

cos(2x)+3sinx+1= 0

cos²x-sin²x+3sin(x)+cos²x+sin²x= 0

2cos²x+3sin(x)= 0

2(1-sin²x)+3sin(x)= 0

2-2sin²x+3sin(x)= 0

2sin²x-3sin(x)-2= 0

sin(x)=t

2t²-3t-2=0

d= 9+16= 25

t1= 2

t2=-1/2

sin(x)=2 нет реш.

sin(x)=-1/2

x=2π/3+2πk, k∈Z