Pertanyaan

Hitunglah: c. tan ( a + b ) ,jika cos a = 5 4 , a lancip, dan sin b = 17 8 , b tumpul.

Hitunglah:

c. $tan (a + b)$ , jika $cos a = \frac{4}{5}$ , $a$ lancip, dan $sin b = \frac{8}{17}$ , $b$ tumpul.

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Jawaban terverifikasi

Pembahasan

, lancip maka: , tumpul maka: Jadi, nilai adalah

, lancip maka:

$begin mathsize 14px style sin space a equals fraction numerator square root of 5 squared minus 4 squared end root over denominator 5 end fraction equals 3 over 5 tan space a equals 3 over 4 end style$

, tumpul maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space b end cell equals cell negative fraction numerator square root of 17 squared minus 8 squared end root over denominator 17 end fraction equals negative 15 over 17 end cell row cell tan space b end cell equals cell negative 8 over 15 end cell end table$

Jadi, nilai adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan open parentheses a plus b close parentheses end cell equals cell fraction numerator tan space a plus tan space b over denominator 1 minus tan space a space tan space b end fraction end cell row blank equals cell fraction numerator begin display style 3 over 4 end style plus begin display style open parentheses negative fraction numerator begin display style 8 end style over denominator begin display style 15 end style end fraction close parentheses end style over denominator 1 minus open parentheses begin display style 3 over 4 end style cross times open parentheses negative begin display style 8 over 15 end style close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 45 over 60 minus 32 over 60 end style over denominator 1 plus begin display style 2 over 5 end style end fraction end cell row blank equals cell fraction numerator begin display style 13 over 60 end style over denominator begin display style 7 over 5 end style end fraction end cell row blank equals cell 13 over 60 cross times 5 over 7 end cell row blank equals cell 13 over 84 end cell end table$