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Diketahui sinA = 3 5 dan sin B = 17 8 , maka nilai dari tan(A-B) adalah...

Diketahui $sinA = \frac{5}{3}$ dan $sin B = \frac{8}{17}$ , maka nilai dari tan(A-B) adalah...

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H. Nufus

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Mahasiswa/Alumni Universitas Negeri Surabaya

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$QA equals square root of PA squared minus PQ squared end root equals square root of 13 squared minus 5 squared end root equals square root of 169 minus 25 end root equals square root of 144 equals 12 tan space straight A equals 5 over 12 BL equals square root of BK squared minus KL squared end root equals square root of 17 squared minus 8 squared end root equals square root of 289 minus 64 end root equals square root of 225 space equals space 15 tan space straight B equals 8 over 15 tan left parenthesis straight A minus straight B right parenthesis equals fraction numerator tan space straight A minus tan space straight B over denominator 1 minus tan space straight A. tan space straight B end fraction equals fraction numerator begin display style 5 over 12 end style minus begin display style 8 over 15 end style over denominator 1 minus begin display style 5 over 12 end style. begin display style 8 over 15 end style end fraction equals fraction numerator begin display style fraction numerator 75 minus 96 over denominator 180 end fraction end style over denominator begin display style fraction numerator 180 minus 40 over denominator 180 end fraction end style end fraction equals negative 21 over 180 straight X space 180 over 140 equals negative 21 over 140$