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Tentukan bentuk sederhana dari cos15∘cot165∘cos75∘sec15∘​=...

Pertanyaan

Tentukan bentuk sederhana dari fraction numerator cos 75 degree sec 15 degree over denominator cos 15 degree cot 165 degree end fraction equals...

Pembahasan:

Sebelumnnya mencari nilai cos 75 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell cos 75 degree end cell equals cell cos open parentheses 45 plus 30 close parentheses end cell row blank equals cell cos 45 cross times cos 30 minus sin 45 cross times sin 30 end cell row blank equals cell 1 half square root of 2 cross times 1 half square root of 3 minus 1 half square root of 2 cross times 1 half end cell row blank equals cell 1 fourth square root of 6 minus 1 fourth square root of 2 end cell row blank equals cell 1 fourth open parentheses square root of 6 minus square root of 2 close parentheses end cell end table

Sebelumnnya mencari nilai cos 15 degree

table attributes columnalign right center left columnspacing 0px end attributes row cell cos 15 degree end cell equals cell cos open parentheses 45 minus 30 close parentheses end cell row blank equals cell cos 45 cross times cos 30 plus sin 45 cross times sin 30 end cell row blank equals cell 1 half square root of 2 cross times 1 half square root of 3 plus 1 half square root of 2 cross times 1 half end cell row blank equals cell 1 fourth square root of 6 plus 1 fourth square root of 2 end cell row blank equals cell 1 fourth open parentheses square root of 6 plus square root of 2 close parentheses end cell end table

Sebelumnnya mencari nilai cot 165

table attributes columnalign right center left columnspacing 0px end attributes row cell cot 165 degree end cell equals cell fraction numerator 1 over denominator tan open parentheses 120 plus 45 close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator tan 120 plus tan 45 over denominator 1 minus tan 120 cross times tan 45 end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator negative square root of 3 plus 1 over denominator 1 minus open parentheses negative square root of 3 plus 1 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 square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 over denominator 1 minus square root of 3 end fraction cross times fraction numerator 1 plus square root of 3 over denominator 1 plus square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 plus square root of 3 plus 3 over denominator 1 plus square root of 3 minus square root of 3 minus 3 end fraction end cell row blank equals cell fraction numerator 4 plus 2 square root of 3 over denominator negative 2 end fraction end cell row blank equals cell negative 2 minus square root of 3 end cell end table

Jadi hasil dari

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos 75 degree sec 15 degree over denominator cos 15 degree cot 165 degree end fraction end cell equals cell fraction numerator begin display style 1 fourth end style open parentheses square root of 6 minus square root of 2 close parentheses cross times 2 open parentheses square root of 6 minus square root of 2 close parentheses over denominator begin display style 1 fourth end style open parentheses square root of 6 plus square root of 2 close parentheses cross times negative 2 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 2 open parentheses square root of 6 minus square root of 2 close parentheses over denominator negative 2 minus square root of 3 end fraction end cell row blank equals cell fraction numerator negative open parentheses square root of 6 minus square root of 2 close parentheses over denominator negative square root of 3 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 6 minus square root of 2 close parentheses over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator square root of 18 minus square root of 6 over denominator 3 end fraction end cell row blank equals cell fraction numerator 3 square root of 2 minus square root of 6 over denominator 3 end fraction end cell row blank equals cell square root of 2 minus square root of 6 end cell end table

 

 

Jawaban terverifikasi

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 06 Oktober 2021

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