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Tunjukan bahwa: c. (cos 2x​−sin 2x​)=1−sin x

Pertanyaan

Tunjukan bahwa:

c. open parentheses cos space x over 2 minus sin space x over 2 close parentheses equals 1 minus sin space x 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

terbukti bahwa, open parentheses cos space x over 2 minus sin space x over 2 close parentheses equals 1 minus sin space x.

Pembahasan

Ingat kembali rumus:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight A over 2 end cell equals cell plus-or-minus square root of fraction numerator 1 minus cos space straight A over denominator 2 end fraction end root end cell row cell cos straight A over 2 end cell equals cell plus-or-minus space square root of fraction numerator 1 plus cos space straight A over denominator 2 end fraction end root end cell end table 

1 minus cos squared straight A equals sin squared space straight A 

open parentheses a minus b close parentheses squared equals a squared plus b squared minus 2 a b open parentheses a minus b close parentheses open parentheses a plus b close parentheses equals a squared minus b squared 

Akan ditunjukkan bahwa, open parentheses cos space x over 2 minus sin space x over 2 close parentheses equals 1 minus sin space x, kita asumsikan sudut x over 2 berada di kuadran pertama, maka cos space x over 2 dan sin space x over 2 bernilai positif, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses cos space x over 2 minus sin space x over 2 close parentheses end cell row blank equals cell open parentheses square root of fraction numerator 1 plus cos space straight A over denominator 2 end fraction end root minus square root of fraction numerator 1 minus cos space straight A over denominator 2 end fraction end root close parentheses squared end cell row blank equals cell fraction numerator 1 plus cos space straight A over denominator 2 end fraction plus fraction numerator 1 minus cos space straight A over denominator 2 end fraction minus 2 open parentheses square root of fraction numerator 1 plus cos space straight A over denominator 2 end fraction end root times square root of fraction numerator 1 minus cos space straight A over denominator 2 end fraction end root close parentheses end cell row blank equals cell 2 over 2 minus 2 square root of fraction numerator open parentheses 1 plus cos space straight A close parentheses open parentheses 1 minus cos space straight A close parentheses over denominator 4 end fraction end root end cell row blank equals cell 1 minus 2 square root of fraction numerator 1 squared minus cos squared straight A over denominator 4 end fraction end root end cell row blank equals cell 1 minus 2 square root of fraction numerator sin squared straight A over denominator 4 end fraction end root end cell row blank equals cell 1 minus fraction numerator up diagonal strike 2 space sinA over denominator up diagonal strike 2 end fraction end cell row blank equals cell 1 minus sin space straight A space bold left parenthesis bold terbukti bold right parenthesis end cell end table   

Jadi, terbukti bahwa, open parentheses cos space x over 2 minus sin space x over 2 close parentheses equals 1 minus sin space x.

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