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Hitunglah: .

Hitunglah: fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction.

Jawaban:

Dalam trigonometri, terdapat sudut-sudut istimewa yang nilainya sudah ada. Berikut adalah tabel nilai sudut istimewa:

Berdasarkan tabel di atas, maka

 fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction equals fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator begin display style fraction numerator 1 over denominator sin space 60 degree end fraction end style times begin display style fraction numerator 1 over denominator tan space 45 degree end fraction end style end fraction equals sin space 60 degree space tan space 45 degree open parentheses sin space 60 degree plus tan space 45 degree plus cos space 30 degree close parentheses equals fraction numerator square root of 3 over denominator 2 end fraction times 1 times open parentheses fraction numerator square root of 3 over denominator 2 end fraction plus 1 plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses equals fraction numerator square root of 3 over denominator 2 end fraction open parentheses 1 plus square root of 3 close parentheses equals fraction numerator square root of 3 over denominator 2 end fraction plus 3 over 2 equals fraction numerator 3 plus square root of 3 over denominator 2 end fraction. 

Dengan demikian, nilai dari fraction numerator sin space 60 degree plus tan space 45 degree plus cos space 30 degree over denominator cosec space 60 degree space cotan space 45 degree end fraction adalah fraction numerator 3 plus square root of 3 over denominator 2 end fraction.

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