Oblicz wartość wyrażenia

[yoana91]

Oblicz: \(\displaystyle{ \frac{sin21 ^{o}cos42 ^{o}+cos21 ^{o}sin42 ^{o} }{cos31 ^{o}cos4 ^{o}+sin31 ^{o}sin4 ^{o}}+sin75 ^{o}+sin15 ^{o}}\)

[czeslaw]

\(\displaystyle{ \frac{\sin 21 ^{\circ}\cos 42 ^{\circ}+\cos 21 ^{\circ}\sin 42 ^{\circ} }{\cos 31 ^{\circ}\cos 4 ^{\circ}+\sin 31 ^{\circ} \sin 4 ^{\circ}}+\sin 75 ^{\circ}+\sin 15 ^{\circ} = \\ \frac{\sin(21^{\circ} + 42^{\circ})}{\cos (31^{\circ} - 4^{\circ})} + \sin (90^{\circ} - 15^{\circ}) + \sin 15^{\circ} = \\ \frac{\sin 63^{\circ}}{\cos 27^{\circ}} + \cos 15^{\circ} + \sin 15^{\circ} = \\\frac{\sin 63^{\circ}}{\cos (90^{\circ} - 63^{\circ})} + \cos 15^{\circ} +\sin 15^{\circ} = \\\frac{\sin 63^{\circ}}{\sin 63 ^{\circ}} + \cos 15^{\circ} +\sin 15^{\circ} = \\1 + \cos 15^{\circ} +\sin 15^{\circ}}\)

P.S. Wyrażenia się nie oblicza, co najwyżej wartość