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Diketahui dan , maka nilai dari tan(A-B) adalah...

Pertanyaan

Diketahui space sinA equals 5 over 3 spacedan sin B equals 8 over 17, maka nilai dari tan(A-B) adalah...

  1. 21 over 140

  2. 20 over 140

  3. negative 18 over 140

  4. negative 20 over 140

  5. negative 21 over 140

Pembahasan Soal:

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

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 22 Desember 2020

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