Buktikan bahwa (cos A+ cos B)² + (sin A + sin B)² = 2+2 cos (A-B)
Matematika
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Pertanyaan
Buktikan bahwa (cos A+ cos B)² + (sin A + sin B)² = 2+2 cos (A-B)
1 Jawaban
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1. Jawaban Anonyme
Identitas Trigonometri.
(cos A + cos B)² + (sin A + sin B)²
= cos² A + 2 cos A cos B + cos² B + (sin² A + 2 sin A sin B + sin² B)
= (cos² A + sin² A) + (cos² B + sin² B) + 2(cos A cos B + sin A sin B)
= 1 + 2 + 2 cos (A - B)
= 2 + 2 cos (A - B)
Terbukti.