1)3sin²π÷2-4tg²π÷4-3cos²π÷6+3ctg²π÷2 2)tg5π÷4×sinπ÷3-cos7π÷6×sin3π÷2 3)sinα=3÷4,0≤α≤π÷2 4)ctgα=2÷3,π≤α≤3π÷2 5)ctgα-cosα-1÷sinα

1) 3 * sin ² (π ÷ 2) - 4 * tg ² (π ÷ 4) - 3 * cos ² (π ÷ 6) + 3 * ctg ² (π ÷ 2) = 3 * 1 ^ 2 - 4 * 1 ^ 2 - 3 * (√3/2) ^ 2 + 3 * 0 ^ 2 = 3 - 4 - 3 * 3/4 = - 1 - 9/4 = - 4/4 - 9/4 = - 13/4;2) tg (5 * π ÷ 4) × sin (π ÷ 3) - cos (7 * π ÷ 6) × sin (3 * π ÷ 2) = 1 * √3/2 - (-√3/2) * (- 1) = √3/2 - √3/2 = 0;3) sin α = 3 ÷ 4, 0 ≤ α ≤ π ÷ 2;cos a = √(1 - sin ^ 2 a) = √(1 - (3/4) ^ 2) = √(1 - 9/16) = √16/16 - 9/16) = √(7/16) = √7/4;4) ctg α = 2 ÷ 3, π ≤ α ≤ 3 * π ÷ 2;tg a = 1/ctg a = 1/(2/3) = 1 * 3/2 = 3/2 = 1,5; 5) ctg α - (cos α - 1) ÷ sin = cos a/sin a - (cos α - 1) ÷ sin = (cos a - (cos a - 1))/sin a = (cos a - cos a + 1)/sin a = 1/sin a;6) (sin β × ctg β) ² + (cos β × tgβ) ² = (sin β × cos β/sin β) ² + (cos β × sin β/cosβ) ² = cos ^ 2 β + sin ^ 2 β = 1.