Question

Вычислите :
2sin 127°+cos 37° - 8cos 143°/sin 42° * sin 75°+sin 48*sin 15°

Answer 1

$\displaystyle \frac{2\sin127^\circ+\cos37^\circ-8\cos143^\circ}{\sin42^\circ\sin75^\circ+\sin48^\circ\sin15^\circ}=\frac{2\sin(90^\circ+37^\circ)+\cos37^\circ-8\cos(180^\circ-37^\circ)}{\sin(90^\circ-48^\circ)\sin(90^\circ-15^\circ)+\sin48^\circ\sin15^\circ}=\\ \\ =\frac{2\cos37^\circ+\cos37^\circ+8\cos37^\circ}{\cos48^\circ\cos15^\circ+\sin48^\circ\sin15^\circ}=\frac{11\cos37^\circ}{\cos(48^\circ-15^\circ)}=\frac{11\cos37^\circ}{\cos33^\circ}$