Pertanyaan

sec ( θ − 2 π ) ⋅ sin ( 54 0 ∘ + θ ) ⋅ cot ( θ − 9 0 ∘ ) cos ( 9 0 ∘ + θ ) ⋅ sec ( 2 π − θ ) ⋅ tan ( π − θ ) = ....

$\frac{cos ( 9 0 ^{\circ} + θ ) \cdot sec ( 2 π - θ ) \cdot tan ( π - θ )}{sec ( θ - 2 π ) \cdot sin ( 54 0 ^{\circ} + θ ) \cdot cot ( θ - 9 0 ^{\circ} )}$ = ....

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat kembali identitas dasar trigonometri berikut. dan sifat relasi kuadran pada perbandingan trigonometri berikut. Maka, diperoleh perhitungan berikut ini. Dengan demikian, hasil dari adalah 1. Oleh karena itu, jawaban yang benar adalah C.

Ingat kembali identitas dasar trigonometri berikut.

$sec space straight theta equals fraction numerator 1 over denominator cos space straight theta end fraction$

$cot space straight theta equals fraction numerator 1 over denominator tan space straight theta end fraction$

$cot space straight theta equals fraction numerator cos space straight theta over denominator sin space straight theta end fraction$

dan sifat relasi kuadran pada perbandingan trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 90 degree plus straight theta close parentheses end cell equals cell negative sin space straight theta end cell row cell tan space open parentheses straight pi minus straight theta close parentheses end cell equals cell negative cot space straight theta end cell end table

Maka, diperoleh perhitungan berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space open parentheses 90 degree plus straight theta close parentheses times sec space open parentheses 2 straight pi minus straight theta close parentheses times tan space open parentheses straight pi minus straight theta close parentheses over denominator sec space open parentheses straight theta minus 2 straight pi close parentheses times sin space open parentheses 540 degree plus straight theta close parentheses times cot space open parentheses straight theta minus 90 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative sin space straight theta times begin display style fraction numerator 1 over denominator cos space open parentheses 2 straight pi minus straight theta close parentheses end fraction end style times open parentheses negative cot space straight theta close parentheses over denominator begin display style fraction numerator 1 over denominator cos space open parentheses straight theta minus 2 straight pi close parentheses end fraction end style times sin space open parentheses 180 degree plus straight theta close parentheses times begin display style fraction numerator 1 over denominator tan space open parentheses straight theta minus 90 degree close parentheses end fraction end style end fraction end cell row blank equals cell fraction numerator negative sin space straight theta times begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style times open parentheses begin display style fraction numerator negative cos space straight theta over denominator sin space straight theta end fraction end style close parentheses over denominator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style times open parentheses negative sin space straight theta close parentheses times begin display style fraction numerator 1 over denominator tan space open parentheses negative open parentheses 90 degree minus straight theta close parentheses close parentheses end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator negative sin space straight theta over denominator cos space straight theta end fraction end style times begin display style fraction numerator 1 over denominator negative tan space open parentheses 90 degree minus straight theta close parentheses end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator negative sin space straight theta over denominator cos space straight theta end fraction end style times begin display style fraction numerator 1 over denominator negative tan space straight theta end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator negative sin space straight theta over denominator cos space straight theta end fraction end style times begin display style fraction numerator cos space straight theta over denominator negative sin space straight theta end fraction end style end fraction end cell row blank equals cell 1 over 1 end cell row blank equals 1 end table$

Dengan demikian, hasil dari $fraction numerator cos space open parentheses 90 degree plus straight theta close parentheses times sec space open parentheses 2 straight pi minus straight theta close parentheses times tan space open parentheses straight pi minus straight theta close parentheses over denominator sec space open parentheses straight theta minus 2 straight pi close parentheses times sin space open parentheses 540 degree plus straight theta close parentheses times cot space open parentheses straight theta minus 90 degree close parentheses end fraction$ adalah 1.

Oleh karena itu, jawaban yang benar adalah C.