oblicz
: 24 maja 2016, 19:10
oblicz:
\(\frac{3sin1575-4cos450}{cos720-sin(-600)}\)
\(\frac{3sin1575-4cos450}{cos720-sin(-600)}\)
alibaba8000 pisze:oblicz:
\(\frac{3sin1575-4cos450}{cos720-sin(-600)}\)
\(...=\frac{3\sin (4\cdot 360^{\circ}+135^{\circ})-4\cos (360^{\circ}+90^{\circ})}{\cos (2\cdot 360^{\circ})+\sin (360^{\circ}+240^{\circ})}=\frac{3\sin 135^{\circ}-4\cos 90^{\circ}}{\cos 0^{\circ}+\sin 240^{\circ})}=\\=\frac{3\sin (180^{\circ}-45^{\circ})}{1+\sin (270^{\circ}-30^{\circ})}=\frac{3\sin 45^{\circ}}{1-\cos 30^{\circ}}=\frac{3\cdot\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{3}}{2}}=\frac{3\sqrt{2}}{2}\cdot\frac{2}{2-\sqrt{3}}=3\sqrt{6}+6\sqrt{2}\)