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Pertanyaan

Jika tan space theta equals a  untuk theta sudut lancip, nilai  cos space 3 theta sama dengan...

  1. open parentheses fraction numerator 1 minus 3 a squared over denominator 1 plus a squared end fraction close parentheses square root of 1 plus a squared end root

  2. open parentheses fraction numerator 1 minus 3 a squared over denominator open parentheses 1 plus a close parentheses squared end fraction close parentheses square root of 1 plus a squared end root

  3. open parentheses fraction numerator 1 plus 3 a squared over denominator 1 plus a squared end fraction close parentheses square root of 1 plus a squared end root

  4. open parentheses fraction numerator 1 minus 3 a squared over denominator open parentheses 1 plus a squared close parentheses squared end fraction close parentheses square root of 1 plus a squared end root

  5. open parentheses fraction numerator 1 plus 3 a squared over denominator open parentheses 1 plus a squared close parentheses squared end fraction close parentheses square root of 1 plus a squared end root

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat rumus-rumus trigonometri berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis straight A plus straight B right parenthesis end cell equals cell cos space straight A space cos space straight B space minus space sin space straight A space sin space straight B end cell row cell cos space 2 straight A end cell equals cell 2 cos squared space straight A minus 1 end cell row cell sin space 2 straight A end cell equals cell 2 space sin space straight A space cos space straight A end cell end table

Berdasarkan rumus di atas, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 3 theta end cell equals cell cos space open parentheses 2 theta plus theta close parentheses end cell row blank equals cell cos space 2 theta space cos space theta minus sin space 2 theta space sin space theta end cell row blank equals cell open parentheses 2 cos squared space theta minus 1 close parentheses space cos space theta minus space 2 space sin space theta space cos theta space sin space theta end cell row blank equals cell 2 cos cubed space theta minus cos space theta minus 2 sin squared space theta space cos space theta end cell end table

Selanjutnya diketahui bahwa tan space theta equals a dan theta sudut lancip, dengan segitiga siku-siku bantu,

Sehingga,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 3 theta end cell equals cell 2 cos cubed space theta minus cos space theta minus 2 sin squared space theta space cos space theta end cell row blank equals cell 2 open parentheses fraction numerator 1 over denominator square root of 1 plus a squared end root end fraction close parentheses cubed minus fraction numerator 1 over denominator square root of 1 plus a squared end root end fraction minus 2 open parentheses fraction numerator a over denominator square root of 1 plus a squared end root end fraction close parentheses squared open parentheses fraction numerator 1 over denominator square root of 1 plus a squared end root end fraction close parentheses end cell row blank equals cell fraction numerator 2 minus open parentheses 1 plus a squared close parentheses minus 2 a squared over denominator open parentheses 1 plus a squared close parentheses square root of 1 plus a squared end root end fraction end cell row blank equals cell fraction numerator 1 minus 3 a squared over denominator open parentheses 1 plus a squared close parentheses square root of 1 plus a squared end root end fraction cross times fraction numerator square root of 1 plus a squared end root over denominator square root of 1 plus a squared end root end fraction end cell row blank equals cell open parentheses fraction numerator 1 minus 3 a squared over denominator open parentheses 1 plus a squared close parentheses squared end fraction close parentheses square root of 1 plus a squared end root end cell end table end style

Jadi, jawaban yang tepat adalah D.

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