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12. Sederhanakanlah. f. cos ( x + h ) − cos x

12. Sederhanakanlah.

f.  

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P. Tessalonika

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Mahasiswa/Alumni Universitas Negeri Medan

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Jawaban

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 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus h right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus 1 half h right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 1 half h right parenthesis end cell end table.

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Pembahasan

Ingat rumus identitas selisih cosinus berikut: Dari soal diketahui: x = y = x Sehingga persamaan trigonometri tersebut menjadi: Dengan demikian, .

Ingat rumus identitas selisih cosinus berikut:

cos space x minus cos space y equals negative 2 space sin space 1 half open parentheses x plus y close parentheses space sin space 1 half open parentheses x minus y close parentheses 

Dari soal diketahui:

xopen parentheses x plus h close parentheses 

y = x 

Sehingga persamaan trigonometri tersebut menjadi:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses x plus h close parentheses minus cos space x end cell equals cell negative 2 space sin space 1 half open parentheses open parentheses x plus h close parentheses plus x close parentheses space sin space 1 half open parentheses open parentheses x plus h close parentheses minus x close parentheses end cell row blank equals cell negative 2 space sin space 1 half open parentheses 2 x plus h close parentheses space sin space 1 half open parentheses h close parentheses end cell row blank equals cell negative 2 space sin space open parentheses x plus 1 half h close parentheses space sin space open parentheses 1 half h close parentheses end cell end table end style 

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus h right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x plus 1 half h right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 1 half h right parenthesis end cell end table.

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