1.向量AB=(2,3),向量AC=(1,k),
则BC(-1,k-3)
(1) AB⊥AC时,2*1+3*k=0 解得 k=-2/3
(2) AB⊥BC时,2*(-1)+3*(k-3)=0 解得 k=11/3
(3) AC⊥BC时,1*(-1)+k*(k-3)=0 解得 k=(3±√13)/2
2.f(x)=cos²x+√3sinxcosx+1
=(1/2)cos2x+(√3/2)sin2x+3/2
=sin(2x+π/6)+3/2
最小正周期T=2π/2=π
单增区间2x+π/6∈[2kπ-π/2,2kπ+π/2]
x∈[kπ-π/3,kπ+π/6]
3.cos35°√1-sin20°分之cos20°
=sin70°/[cos35°*√(1-cos70°)]
=√(1-cos²70°)/ [cos35°*√(1-cos70°)]
=√(1+cos70°)/cos35°
=√(2cos²35)/cos35°
=√2