Докажите тождество (sin (a/2) + cos (a/2) ^2/1-sina=ctg^2 (п/4-a/2)

1) cos²a: (sin (a/2) / cos (a/2) - cos (a/2) / sin (a/2) = cos²a: (sin² (a/2) - cos² (a/2) / sin (a/2) cos (a/2) =

cos²a: (-2cosa/sina) = -cos²a*sina/2cosa = - (sinacosa) / 2=-sin2a/4

2) sin (a+π/4) / cos (a+π/4) - sin (a-π/4) / cos (a-π/4) = (sin (a+π/4) cos (a-π/4) - sin (a-π/4) cos (a+π/4)) / cos (a+π/4) cos (a-π/4) =

(sin (a+π/4-a+π/4)) : 1/2 (cos (a+π/4-a+π/4) + cos (a+π/4+a-π/4) =

sinπ/2:1/2 (cosπ/2+cos2a) = 2/cos2a