Нужно вычислить a) sin135*cos210*tg240 / ctg300. b) cos15-sin15. c) sin^2 * П/8 + cos^2 * 3 П/8 + sin^2 * 5 П/3 + cos^2 * 7 П/8

А) Sin 135 = Sin (180 - 45) = Sin 45 = √2/2

Cos 210 = Cos (180 + 30) = - Cos 30 = - √3/2

tg 240 = tg (270 - 30) = Ctg 30 = √3

√2/2 · (-√3/2) ·√3 = 3√2/4

Ctg 300 = Ctg (270 + 30) = - tg 30 = - 1/√3

3√2 : (-1/√3) = - 3√6/4

b) Сos 15 - Sin 15=√ (1+Cos30) / 2 - √ (1 - Сos 30) / 2=

=√ (1+Сos 30) / √2 - √ (1 + Cos 30) / √2 = (√ (1 + √3/2) - √ (1 - √3/2)) / √2=

= (√ (2 + √3) - √ (2 - √3)) / 2

с) Sin²π/8 + Cos²3π/8 + Sin² 5π/8 + Cos² 7π/8 =

= Sin² π/8 + Cos ² 3π/8 + Sin² 3π/8 + Cos² π/8 = 1 + 1 = 2