1. Oblicz: a) 2(sin²15°+cos²15°) - 3tg30° / 2sin45°= sin²15°+cos²15° = 1( jedynka trygonometryczna) = 2*1 - 3*(1/3)*√3 : 2*(1/2)*√2= = 2 - √3 : √2 = = 2 - √(3/2)= = 2 - (√3*√2):2= = 2 - √6 : 2= = 2 -(1/2)*√6 b) sin225° - ctg495°= = sin (180° +45°) - ctg (360° +135°)= = - sin 45° - ctg 135° = = -1/2*√2 - ctg (180° -45°) = = -1/2*√2 - (-ctg 45°) = = -1/2*√2 + 1 = = 1 - 1/2√2 2 Udowodnij: (L=P) a) tgx + cosx / 1+sinx = 1 / cosx L = tgx + cosx / 1+sinx L = sin x : cos x + cos x :(1 + sinx) sprowadzam do wspólnego mianownika L = [sin x *( 1+sin x)] : [ cos x *(1+sinx)] + (cos x* cos x) : [ cos x *(1+sinx)] L = [sin x *( 1+sin x) + cosx *cosx)] : [cos x *( 1+sin x)] L = [ sin x + sin²x + cos²x ] : [cos x *( 1+sin x)] sin²x + cos² x =1 L = [ sin x +1] : [cos x *( 1+sin x)] L = [ 1 + sin x] : [cos x *( 1+sin x)] L = 1 : cos x L = 1/cosx P = 1/cos x L = P b) (sinx+cosx)²+(sinx-cosx)²= = (sin²x + 2*sinx*cosx + cos²x) + (sin²x - 2*sinx*cosx + cos²x)= = sin²x + 2*sinx*cosx + cos²x + sin²x - 2*sinx*cosx + cos²x = = sin²x + cos²x + sin²x + cos²x= sin²x + cos²x =1 = 1 + 1 = 2
