1. 2sin60*tg30-cosπ=2*√3/2*1/√3-(-1)=1+1=2
cos(-420)=cos420=cos(360+60)=cos60=1/2
sin840=sin(2*360+120)=sin(120)=sin(90+30)=cos30=√3/2
2cos²15* sin15/cos15=2sin15*cos15=sin30=1/2
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2. sin 180=0 cos13π/7=cos(2π-π/7)=cos(-π/7)=cos(π/7)>0
cos(13π/7)>sin180
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cos2π/3 ∨ 2π/3 2π/3≈2 2π/3>cos(2π/3)
3. max 3sina-1=3*1-1=2 min 3sina-1=-3*1-1=-4
4. cosa=12/13 a∈(0;π/2) sina=√(1-12²/13²)=√((169-144)/13²)=1/13*√25=
5/13; tga=sina/cosa=5/13*13/12=5/12 ctga=1/tga=12/5
5. легко но долго.
6. 2cosx=√2 cosx=√2/2 x=+-π/4+2πk k∈Z
sin(x+π/6)=-1 x+π/6=(-1)ⁿ*1/2+πn x=(-1)ⁿ*1/2-π/6+πn n∈Z
ctg(x/3)=-√3/3 сtg(-x/3)=√3/3 -x/3=π/3+πn -x=π+3πn
x=-π-3πn n∈Z