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

Question

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

Answer 1

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