PEMBAHASAN
Trigonometri
sin A + sin B = 2 sin (A + B)/2 cos (A - B)/2
cos A + cos B = 2 cos (A + B)/2 cos (A - B)/2
pembilang
sin (60 - a)° + sin (60 + a)°
= 2 sim (60 - a + 60 + a)°/2 cos (60 - a - (60 + a))°/2
= 2 sin (120°/2) cos (-2a/2)°
= 2 sin 60° cos (-a)°
= 2 sin 60° cos a°
penyebut
cos (30 + a)° + cos (30 - a)°
= 2 cos (30 + a + 30 - a)/2 cos (30 + a - (30 - a))/2
= 2 cos (60°/2) cos (2a/2)°
= 2 cos 30° cos a°
= 2 sin (90° - 30°) cos a°
soal
= pembilang / penyebut
= 2 sin 60° cos a° / (2 sin 60° cos a°)
= 1
__
cos (-a) = cos a
cos a = sin (90° - a)
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PEMBAHASAN
Trigonometri
sin A + sin B = 2 sin (A + B)/2 cos (A - B)/2
cos A + cos B = 2 cos (A + B)/2 cos (A - B)/2
pembilang
sin (60 - a)° + sin (60 + a)°
= 2 sim (60 - a + 60 + a)°/2 cos (60 - a - (60 + a))°/2
= 2 sin (120°/2) cos (-2a/2)°
= 2 sin 60° cos (-a)°
= 2 sin 60° cos a°
penyebut
cos (30 + a)° + cos (30 - a)°
= 2 cos (30 + a + 30 - a)/2 cos (30 + a - (30 - a))/2
= 2 cos (60°/2) cos (2a/2)°
= 2 cos 30° cos a°
= 2 sin (90° - 30°) cos a°
= 2 sin 60° cos a°
soal
= pembilang / penyebut
= 2 sin 60° cos a° / (2 sin 60° cos a°)
= 1
__
cos (-a) = cos a
cos a = sin (90° - a)