1.
а) 2sin60°+ctg(-π/6)-cos0=2* √3 - √3 - 1 = -1
2
б) √3 cos(-5π/6) - sin570° =
=√3 cos(π -π/6) - sin(360°+180°+30°)=
=√3 (-cosπ/6) - sin(180°+30°)=
=-√3 * √3 - (-sin30°) = -3 + 1 = -1
2 2 2
2.
a) sin⁴α+sin²α cos²α -sin²α =
= sin²α (sin²α+cos²α- 1)=
= sin²α (1-1)=0
б) 1 + ctg²(π-α)+ctg(π/2 -α) tg(3π/2 +α) =
cos²(π-α)
= 1 + (-ctgα)² + tgα * (-tgα) =
(-cosα)²
= 1 + ctg²α - tg²α =
cos²α
= tg²α +1 +ctg²α - tg²α =1 + ctg²α = 1
sin²α
3.
tgα =3/4 180°<α<270°<br> cos(180°+α)=-cosα
1 = tg²α +1
cos²α
1 = (3/4)² +1
cos²α
1 = 9 + 16
cos²α 16 16
1 = 25
cos²α 16
cos²α = 16
25
cosα = + 4/5
Угол α находится в 3-ей четверти,
cosα имеет знак "-".
cosα = -4/5
-cosα = 4/5
Ответ: 4/5.
4. tg15° tg30° tg45° tg60° tg75° = 1*tg45°*1=1
1) tg75°=tg(90°-15°)=ctg15°
2) tg15° ctg15° =1
3) tg60°=tg(90°-30°)=ctg30°
4) tg30° ctg30°=1