Много за решение. №1. выражение: 1. (1+tg²α)cos²α; 2. tgα+tgβ/ctgα+ctgβ; 3. cos³α-ctg²α/sin²α-tg²α. №2. найдите значение выражения: 1. sin 3π/4 cos 3π/4 - tg 3π/4 + 1.5ctg 3π/4; 2. tg² 2π/3 - ctg² 2π/3 - 10/3 sin² 2π/3 + cos² 2π/3; 3. 4 cos 5π/6 sin 5π/6 + 3tg² 5π/6; 4. tg 3π/4 sin 3π/2 - ctg π/2 cos π/6.
1. (1+tg²α)cos²α =
2. tgα+tgβ/ctgα+ctgβ = tgα*tgβ
3. cos³α-ctg²α/sin²α-tg²α = tg²α
№2
1. sin 3π/4 cos 3π/4 - tg 3π/4 + 1.5ctg 3π/4 = √2/2 *(-√2/2 ) + 1 - 1,5 = -0,5 + 1 -1,5 = -1
2. tg² 2π/3 - ctg² 2π/3 - 10/3 sin² 2π/3 + cos² 2π/3 = 3 - 1/3 - 10/3 * 3/4 + 1/4 = 5/12
3. 4 cos 5π/6 sin 5π/6 + 3tg² 5π/6 = 4* (-√3/2)* 1/2 + 3* 3/9 = -√3
4. tg 3π/4 sin 3π/2 - ctg π/2 cos π/6 = (-1) * √2/2 - 0 = -√2/2