Nilai dari sin 225°+sin15°/cos225°+cos 15° adalah...

sin 225° + sin 15° = 2 sin [1/2 (225° + 15°)] cos [1/2 (225° - 15°)]
= 2 (1/2 √3) [1/4 (√2 - √6)]
= 1/4 (√6 - 3√2)

cos 225° + cos 15° = 2 cos [1/2 (225 + 15)°] cos [1/2 (225 - 15)°]
= 2 (-1/2) [1/4 (√2 - √6)]
= 1/4 (√6 - √2)

(sin 225° + sin 15°) / (cos 225° + cos 15°)
= [1/4 (√6 - 3√2)] / [1/4 (√6 - √2)]
= (√6 - 3√2) / (√6 - √2) [(√6 + √2) / (√6 + √2)]
= -4√3 / 4
= -√3 ← Jawaban

Catatan:
cos 105° = cos (60 + 45)°
= cos 60° cos 45 ° - sin 60° sin 45°
= (1/2)(1/2 √2) - 1/2 √3 (1/2 √2)
= 1/4 (√2 - √6)