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Diketahui a dan b adalah sudut lancip. Jika a plus b equals straight pi over 4 dan tan space b equals 1 third space tan space a maka tan space open parentheses a minus b close parentheses=....

  1. negative fraction numerator 4 square root of 7 over denominator 7 end fraction

  2. negative fraction numerator 3 square root of 7 over denominator 7 end fraction

  3. fraction numerator square root of 7 over denominator 7 end fraction

  4. fraction numerator 2 square root of 7 over denominator 7 end fraction

  5. fraction numerator 3 square root of 7 over denominator 7 end fraction

N. Puspita

Master Teacher

Jawaban terverifikasi

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Ingat

tan open parentheses x plus y close parentheses equals fraction numerator tan space x plus tan space y over denominator 1 minus tan space x space tan space y end fraction tan open parentheses x minus y close parentheses equals fraction numerator tan space x minus tan space y over denominator 1 plus tan space x space tan space y end fraction

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses a plus b close parentheses end cell equals cell fraction numerator tan space a plus tan space b over denominator 1 minus tan space a times space tan space b end fraction end cell row cell tan space open parentheses straight pi over 4 close parentheses end cell equals cell fraction numerator 3 space tan space b plus tan space b over denominator 1 minus 3 space tan space b times space tan space b end fraction end cell row cell tan space open parentheses straight pi over 4 close parentheses end cell equals cell fraction numerator 3 space tan space b plus tan space b over denominator 1 minus 3 space tan space b times space tan space b end fraction end cell row 1 equals cell fraction numerator 4 space tan space b space space over denominator 1 minus space 3 space tan squared space b end fraction end cell row cell 3 space tan squared b plus 4 space tan space b minus 1 end cell equals 0 row cell tan space b subscript 1 comma space 2 end subscript end cell equals cell fraction numerator negative 4 plus-or-minus square root of 16 plus 12 end root over denominator 6 end fraction end cell row cell tan space b subscript 1 comma space 2 end subscript end cell equals cell fraction numerator negative 2 plus-or-minus square root of 7 over denominator 3 end fraction end cell row cell tan space b end cell equals cell fraction numerator negative 2 plus square root of 7 over denominator 3 end fraction open parentheses lancip close parentheses end cell row cell tan space a end cell equals cell space minus 2 plus square root of 7 end cell row blank blank blank row cell tan space open parentheses a minus b close parentheses end cell equals cell fraction numerator tan space a space minus tan space b over denominator 1 minus tan space a times tan space b end fraction end cell row blank equals cell fraction numerator negative 2 plus square root of 7 minus open parentheses fraction numerator negative 2 plus square root of 7 over denominator 3 end fraction close parentheses over denominator 1 minus open parentheses negative 2 plus square root of 7 close parentheses open parentheses fraction numerator negative 2 plus square root of 7 over denominator 3 end fraction close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 plus square root of 7 over denominator 7 minus 2 square root of 7 end fraction end cell row blank equals cell fraction numerator negative 2 plus square root of 7 over denominator 7 minus 2 square root of 7 end fraction times fraction numerator 7 plus 2 square root of 7 over denominator 7 plus 2 square root of 7 end fraction end cell row blank equals cell fraction numerator 3 square root of 7 over denominator 21 end fraction end cell row blank equals cell fraction numerator square root of 7 over denominator 7 end fraction end cell end table

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