2. (2*sin²α-1) /(sinα-cosα)=(2*sin²α-sin²α-cos²α)/(sinα-cosα)=
=(sin²α-cos²α)/(sinα-cosα)=(sinα+cosα)*(sinα-cosα)/(sinα-cosα)=sinα+cosα.
4. (sinα)⁻¹+(tgα)⁻¹=ctgα/2
1/sinα+cosα/sinα=(1+cosα)/sinα=ctgα/2=
=(sin²α/2+cos²α/2+cos²α/2-sin²α/2)/(2*sinα/2*cosα/2)=
=2*cos²α/2/(2*sinα/2*cosα/2)=cosα/sinα=ctgα/2.
7. (tg(x/2)-√3)/sin(4x)<0 ОДЗ sin4x≠0 x≠πn/4<br>tg(x/2)-√3>0 tg(x/2)>√3 x/2>π/3 x>(2/3)π
sin(4x)<0 4x<0 x<0 <strong> x∉
tg(x/2)-√3<0 tg(x/2)<√3 x/2<π/3 x<(2/3)π<br>sin(4x)>0 4x>0 x>0 x∈(0;(2/3)π).