Pertanyaan

cot 105° tan 15° = ....

R. Rohmat

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cot invisible function application 105 degree tan invisible function application 15 degree end cell equals cell fraction numerator cos invisible function application 105 degree over denominator sin invisible function application 105 degree end fraction ⋅ fraction numerator sin invisible function application 15 degree over denominator cos invisible function application 15 degree end fraction end cell row blank equals cell fraction numerator cos invisible function application 105 degree sin invisible function application 15 degree over denominator sin invisible function application 105 degree cos invisible function application 15 degree end fraction end cell row blank equals cell fraction numerator 1 half open parentheses sin invisible function application open parentheses 105 degree plus 15 degree close parentheses minus sign sin invisible function application open parentheses 105 degree minus sign 15 degree close parentheses close parentheses over denominator 1 half open parentheses sin invisible function application open parentheses 105 degree plus 15 degree close parentheses plus sin invisible function application open parentheses 105 degree minus sign 15 degree close parentheses close parentheses end fraction end cell row blank equals cell fraction numerator sin invisible function application 120 degree minus sign sin invisible function application 90 degree over denominator sin invisible function application 120 degree plus sin invisible function application 90 degree end fraction end cell row blank equals cell fraction numerator 1 half square root of 3 minus sign 1 over denominator 1 half square root of 3 plus 1 end fraction end cell row blank equals cell fraction numerator 1 half square root of 3 minus sign 1 over denominator 1 half square root of 3 plus 1 end fraction ⋅ 2 over 2 end cell row blank equals cell fraction numerator square root of 3 minus sign 2 over denominator square root of 3 plus 2 end fraction end cell row blank equals cell fraction numerator square root of 3 minus sign 2 over denominator square root of 3 plus 2 end fraction ⋅ fraction numerator square root of 3 minus sign 2 over denominator square root of 3 minus sign 2 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 3 minus sign 2 close parentheses open parentheses square root of 3 minus sign 2 close parentheses over denominator open parentheses square root of 3 plus 2 close parentheses open parentheses square root of 3 minus sign 2 close parentheses end fraction end cell row blank equals cell fraction numerator 3 minus sign 4 square root of 3 plus 4 over denominator 3 minus sign 4 end fraction end cell row blank equals cell fraction numerator 7 minus sign 4 square root of 3 over denominator negative sign 1 end fraction end cell row blank equals cell negative sign 7 plus 4 square root of 3 end cell end table end style$

Jadi, jawaban yang tepat adalah A.

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