Объяснение:
1) tg(180°+α)-ctg(270°-α)=tgα-(-ctgα)=tgα+ctgα=(sinα/cosα)+(cosα/sinα)=
=(sin²α+cos²α)/(sinα*cosα)=1/(sinα*cosα)=2*1/(2*(sinα*cosα)=2/sin(2α).
2)sin(180-α)*ctg(360+α)=sinα*ctgα=sinα*(cosα/sinα)=cosα.
3) cos(2π-α)-sin(3π/2-α)=cosα-(-cosα)=cosα+cosα)=2*cosα.
4) tg(3π/2-α)*ctg(π/2-α)=tgα*ctgα=(sinα/cosα)*(cosα/sinα)=1.
Объяснение:
1) tg(180°+α)-ctg(270°-α)=tgα-(-ctgα)=tgα+ctgα=(sinα/cosα)+(cosα/sinα)=
=(sin²α+cos²α)/(sinα*cosα)=1/(sinα*cosα)=2*1/(2*(sinα*cosα)=2/sin(2α).
2)sin(180-α)*ctg(360+α)=sinα*ctgα=sinα*(cosα/sinα)=cosα.
3) cos(2π-α)-sin(3π/2-α)=cosα-(-cosα)=cosα+cosα)=2*cosα.
4) tg(3π/2-α)*ctg(π/2-α)=tgα*ctgα=(sinα/cosα)*(cosα/sinα)=1.