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PERTANYAAN :

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begin mathsize 12px style fraction numerator 1 over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator 1 over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator 1 over denominator cos space 88 degree space times space cos space 89 degree end fraction equals fraction numerator cos space 1 degree over denominator sin squared space 1 degree end fraction end stylespace space 

Jawaban

terbukti bahwa begin mathsize 12px style fraction numerator 1 over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator 1 over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator 1 over denominator cos space 88 degree space times space cos space 89 degree end fraction equals fraction numerator cos space 1 degree over denominator sin squared space 1 degree end fraction end style.space space 


Ingat,

Tangen sudut

tan space x equals fraction numerator sin space x over denominator cos space x end fraction

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space A space minus space tan space B space end cell equals cell fraction numerator sin space A over denominator cos space A end fraction minus fraction numerator sin space B over denominator cos space B end fraction end cell row cell tan space A space minus space tan space B space end cell equals cell fraction numerator sin space A space cos space B space minus space sin space B space cos space A over denominator cos space A space cos space B end fraction end cell row cell tan space A space minus space tan space B space end cell equals cell fraction numerator sin space open parentheses A minus B close parentheses over denominator cos space A space cos space B end fraction end cell end table

Berdasarkan rumus tersebut, diperoleh sebagai berikut

Buktikan

begin mathsize 12px style fraction numerator 1 over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator 1 over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator 1 over denominator cos space 88 degree space times space cos space 89 degree end fraction equals fraction numerator cos space 1 degree over denominator sin squared space 1 degree end fraction end style

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank equals cell fraction numerator 1 over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator 1 over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator 1 over denominator cos space 88 degree space times space cos space 89 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets fraction numerator sin space 1 degree over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator sin space 1 degree over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator sin space 1 degree over denominator cos space 88 degree space times space cos space 89 degree end fraction close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets fraction numerator sin space 1 degree over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator sin space 1 degree over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator sin space 1 degree over denominator cos space 88 degree space times space cos space 89 degree end fraction close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets fraction numerator sin space open parentheses 1 minus 0 close parentheses degree over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator sin space open parentheses 2 minus 1 close parentheses degree over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator sin space open parentheses 89 minus 88 close parentheses degree over denominator cos space 88 degree space times space cos space 89 degree end fraction close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets open parentheses tan space 1 degree minus tan space 0 degree close parentheses plus open parentheses tan space 2 degree minus tan space 1 degree close parentheses plus... plus open parentheses tan space 89 degree minus tan space 88 degree close parentheses close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets negative tan space 0 degree plus tan space 89 degree close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets tan space 89 degree close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets tan space open parentheses 90 minus 1 close parentheses degree close square brackets end cell row blank equals cell fraction numerator 1 over denominator sin space 1 degree end fraction open square brackets c o tan space 1 degree close square brackets end cell row blank equals cell fraction numerator cos space 1 degree over denominator sin squared space 1 degree end fraction end cell end table end style

Dengan demikian, terbukti bahwa begin mathsize 12px style fraction numerator 1 over denominator cos space 0 degree space times space cos space 1 degree end fraction plus fraction numerator 1 over denominator cos space 1 degree space times space cos space 2 degree end fraction plus... plus fraction numerator 1 over denominator cos space 88 degree space times space cos space 89 degree end fraction equals fraction numerator cos space 1 degree over denominator sin squared space 1 degree end fraction end style.space space 


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