1 sina =2*tan(a/2)]/{1 +[tan(a/2)]^2}
cosa ={1 -[tan(a/2)]^2}/{1 +[tan(a/2)]^2}
代入sina+cosa=1/5,解得:tan(a/2) =2,[tan(a/2) >0]
==> tana =[2*tan(a/2)]/{1 -[tan(a/2)]^2} = -4/3
3.
4.
5.y=cos²x+2sinxcosx+3sin²x
=1+sin(2x)+2sin²x
=sin(2x)+cos(2x)
=√2sin(2x+π/4)
最小正周期Tmin=2π/2=π
当sin(2x+π/4)=-1时,有ymin=-√2
2kπ-π/2≤2x+π/4≤2kπ+π/2 (k∈Z)时,即kπ-3π/8≤x≤kπ+π/8 (k∈Z)时,函数单调递增.
单调递增区间为[kπ-3π/8,kπ+π/8] (k∈Z)
] 1 sina =2*tan(a/2)]/{1 +[tan(a/2)]^2}
cosa ={1 -[tan(a/2)]^2}/{1 +[tan(a/2)]^2}
代入sina+cosa=1/5,解得:tan(a/2) =2,[tan(a/2) >0]
==> tana =[2*tan(a/2)]/{1 -[tan(a/2)]^2} = -4/3
3.
4.
5.y=cos²x+2sinxcosx+3sin²x
=1+sin(2x)+2sin²x
=sin(2x)+cos(2x)
=√2sin(2x+π/4)
最小正周期Tmin=2π/2=π
当sin(2x+π/4)=-1时,有ymin=-√2
2kπ-π/2≤2x+π/4≤2kπ+π/2 (k∈Z)时,即kπ-3π/8≤x≤kπ+π/8 (k∈Z)时,函数单调递增.
单调递增区间为[kπ-3π/8,kπ+π/8] (k∈Z)
]