1.
-1=tan(α＋β)＝tanα+tanβ/(1-tanαtanβ）
tanαtanβ-1=tanα+tanβ）
tanαtanβ-tanα-tanβ=1
tanαtanβ-tanα-tanβ+=2
(1-tanα)(1-tanβ）=2
2.
sin^4θ＋cos^4θ＝(sin^2θ＋cos^2θ)^2-2sin^2θcos^2θ
=1-(1/2)*(2sinθcosθ)^2
=1-(sin2θ)^2/2=5/9
sin2θ=2√2/3 sin2θ=-2√2/3
3.
sin(α/2)-cos(α/2)＝1/5,两边平方得
1－sinα=1/25
sinα=24/25
f(X)＝sin(X＋π/6)＋sin(X-π/6)＋cosX＋a
=2sinxcosπ/6+cosx+a
=√3sinx+cosx+a
=2sin(x+π/6)+a
最大值为1
a=-1
f(X)≥0
sin(x+π/6)≥1/2
2kπ+π/6≤x+π/6≤2kπ+5π/6
2kπ≤x≤2kπ+2π/3