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Jika  dan , maka  adalah ....

Jika begin mathsize 14px style tan space A equals 1 half end style dan begin mathsize 14px style tan space B equals 1 third end style, maka begin mathsize 14px style tan space open parentheses A plus B close parentheses end style adalah .... 

  1. begin mathsize 14px style 1 half square root of 2 end style 

  2. size 14px 1 over size 14px 2 square root of size 14px 3 

  3. size 14px 1 over size 14px 3 square root of size 14px 2  

  4. begin mathsize 14px style 1 third square root of 3 end style  

  5. size 14px 1 

Jawaban:

Gunakan rumus jumlah sudut pada tangen.

Diketahui:

begin mathsize 14px style tan space A equals 1 half end style dan begin mathsize 14px style tan space B equals 1 third end style.

Alkan ditentukan nilai dari begin mathsize 14px style tan space open parentheses A plus B close parentheses end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space open parentheses straight A plus straight B close parentheses end cell equals cell fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A space tan space straight B end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style 1 third end style over denominator 1 minus open parentheses begin display style 1 half end style cross times begin display style 1 third end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 3 plus 2 over denominator 6 end fraction end style over denominator 1 minus begin display style 1 over 6 end style end fraction end cell row blank equals cell fraction numerator begin display style 5 over 6 end style over denominator begin display style fraction numerator 6 minus 1 over denominator 6 end fraction end style end fraction end cell row blank equals cell fraction numerator up diagonal strike begin display style 5 over 6 end style end strike over denominator up diagonal strike begin display style 5 over 6 end style end strike end fraction end cell row blank equals cell 1 over 1 end cell row cell tan space open parentheses straight A plus straight B close parentheses end cell equals 1 end table end style 

Jadi, jawaban yang tepat adalah E.

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