Question

1. Uzasadnij równość :
a) sin² 25° + sin² 65° = 1
b) cos 17° - sin 73° = 0
c) tg 15° * tg 45° * tg 75° = 1
d) tg 66° * cos 66° - cos 24° = 0

Answer 1

Sin(90-alfa) = cos(alfa)
a) sin25 = sin(90-65) = cos65, a więc będzie: cos²65 + sin²65 = 1
b) sin73 = sin(90-17) = cos17, a więc będzie: cos17 - cos17 = 0
c) tg(90-alfa) = ctg alfa, więc  tg75 = tg(90-15) = ctg15
tga = sina/cosa, ctga = cosa/sina, a więc tga * ctga = 1
tg45 = 1. a więc:
tg15 * tg75 * tg45 = 1 * 1 = 1
d) tga = sina/cosa -> sina = tga * cosa, a więc:
tg66*cos66 = sin66
sin66 - cos24 = 0 - to już analogicznie jak w b