Вычислить:

(cos 75 град - sin 75 град) в квадрате

tg п/8 делить на 1-tg^2 п/8

1) (cos75° - sin75°) ² = cos²75° - 2sin75°cos75° + cos²75° = 1 - 2sin (2*75°) =

= 1 - 2sin (180° - 30°) 1 - 2*sin30° = 1 - 2 * (1/2) = 1 - 1 = 0

2) tg (п/8) / (1 - tg ² (п/8)) = (1/2) * [2 tg (п/8) / (1 - tg² (п/8)) ] = (1/2) * tg2 * (π/8)) =

= (1/2) * tg (π/4) = (1/2) * 1 = 1/2