Question

Oblicz:
a) ctg300° - sin135°
b) ctg300° * sin135°
c) cos225° - tg240°
d) cos225° * tg240°

Oczywiście z użyciem wzorów redukcyjnych. Z góry dziękuję.

Answer 1

Ctg300° = ctg(360°-60°)= ctg(-60°)= -ctg60° = -1/√3
sin135° = sin(180° -45°) =  sin45° = √2/2
cos225°= cos(360°-135°)= cos(-135°)= cos135°= cos(180° -45°)= - cos45°= -√2/2
tg240° = tg(360° -120°) = tg120° = tg(180° -60°) = tg60° = √3

a) ctg300° - sin135° = -1/√3 -√2/2 = -(2+√6)/2√3 = -√3(2+√6)/6
b) ctg300° * sin135° = (-1/√3)*(√2/2) = -√2/2√3 = - √6/6
c) cos225° - tg240° = -√2/2 - √3
d) cos225° * tg240° = (-√2/2)*(√3) = -√6/2