Відповіді АЛГЕБРА: 10.22

10.22

1) tgα+sinα1+cosα = sinαcosα+sinα1+cosα = sinα(1+cosα)cosα1+cosα = sinαcosα = tgα.

2) cosx1+sinx + 1+sinxcosx = cos2x+1+2sinx+sin2xcosx(1+sinx) = 2+2sinxcosx(1+sinx) =

= 2(1+sinx)cosx(1+sinx) = 2cosx

3) sinβ1+cosβ – sinβ1-cosβ = sinβ-sinβcosβ-sinβ-sinβ1+cosβ(1-cosβ) = -2sinβcosβ1- cos2β =

= -2sinβcosβsin2β = –2ctgβ

4) 1+sin⁡(-α)cos⁡(-α) – tg(–α) = 1-sinαcosα = sinαcosα = 1cosα

5) sin⁡(-2x)1-cos⁡(-2x) – ctg(–2x) = -sin2x1-cos2x + cos2xsin2x =

= -sin22x+cos2x- cos22xsin2x(1-cos2x) =cos2x-1sin2x(1-cos2x) = –1sin2x

6) cos2-x4- cos4(-x4)sin2(-x4) = cos2x4- cos4x4sin2x4 = cos2x4(1- cos2x4)sin2x4 =

= cos2x4 • sin2x4sin2x4 = cos²x4