Cos²(π/4 + α) · ctg²(π/4 - α) + sin²(π/4 + α) · tg²(π/4 - α) = 1
Формулы понижения степени:
cos²α = (1 + cos2α)/2
sin²α = (1 - cos2α)/2
(1 + cos(π/2 + 2α)/2) · (1 + cos(π/2 - 2α)) / (1 - cos(π/2 - 2α)) +
+ (1 - cos(π/2 + 2α))/2 · (1 - cos(π/2 - 2α)) / (1 + cos(π/2 - 2α)) = 1
По формулам приведения:
(1 - sin2α)/2 · (1 + sin2α) / (1 - sin2α) + (1 + sin2α)/2 · (1 - sin2α) / (1 + sin 2α) = 1
(1 + sin2α) / 2 + (1 - sin2α )/2 = 1
1/2 + sin2/2 + 1/2 - sin2α/2 = 1
1 = 1