5(sin²x+cos²x-2sinxcosx)-16(sinx-cosx)+3=0
5(sinx-cosx)²-16(sinx-cosx)+3=0
sinx-cosx=t
5t²-16t+3=0, D1=8²-15=64-15=49
t1=(8+7)/5=3,t2=1/5.
1)sinx-cosx=3--не имеет корней
2) sinx -cosx=1/5
√2(1/√2·sinx-1/√2·cosx)=1/5
√2(sinx·cosπ/4-cosx·sinπ/4)=1/5
√2sin(x-π/4)=1/5
sin(x-π/4)=1/(5√2)⇒sin(x-π/4)=√2/10
x-π/4=(-1)^n arcsin√2/10 +πn,n∈Z
x=(-1)^n arcsin√2/10+π/4+πn,n∈Z
5(sin²x+cos²x-2sinxcosx)-16(sinx-cosx)+3=0
5(sinx-cosx)²-16(sinx-cosx)+3=0
sinx-cosx=t
5t²-16t+3=0, D1=8²-15=64-15=49
t1=(8+7)/5=3,t2=1/5.
1)sinx-cosx=3--не имеет корней
2) sinx -cosx=1/5
√2(1/√2·sinx-1/√2·cosx)=1/5
√2(sinx·cosπ/4-cosx·sinπ/4)=1/5
√2sin(x-π/4)=1/5
sin(x-π/4)=1/(5√2)⇒sin(x-π/4)=√2/10
x-π/4=(-1)^n arcsin√2/10 +πn,n∈Z
x=(-1)^n arcsin√2/10+π/4+πn,n∈Z