1
(sin²x+2sinxcosx+cos²x)/(sin²x+cos²x+2sinxcosx)=1
2
2*0-2*0+3*1-0=3
3
1)cos²a-sin²a=cos2a
2)ctg²a-tg²a=cos²a/sin²a-sin²a/*cos²a)=(cos^4a-sin^4a)/cos²asin²a=
=(cos²a-sin²a)(cos²a+sin²a)/sin²acos²a=cos2a/sin²acos²a
3)cos2a:cos2a/sin²acos²a=cos2a *sin²acos²a/cos2a=sin²acos²a
4
а)tg(2x-π/4)=0
2x-π/4=πn
2x=π/4+πn
x=π/8+πn/2,n∈z
в)(2sinx-√2)(2sinx+√2)=0
sinx=√2/2 U sinx=-√2/2
x=+-π/4+2πn,n∈z
c)1-2sin²x=2sin²x
1-4sin²x=0
(1-2sinx)(1+2sinx=0
sinx=1/2 U sinx=-1/2
x=+-π/6+2πn
5
2πn≤x-π/4≤π+2πn
π/4+2πn≤x≤5π/4+2πn