Pertanyaan

Buktikan identitas berikut ini. c. ( csc A − sin A ) ( sec A − cos A ) = cos A sin A

Buktikan identitas berikut ini.

c. $(csc A - sin A) (sec A - cos A) = cos A sin A$

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Pembahasan

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$begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses csc space A minus sin space A close parentheses open parentheses sec space A minus cos space A close parentheses end cell equals cell fraction numerator 1 over denominator sin space A end fraction times fraction numerator 1 over denominator cos space A end fraction minus fraction numerator 1 over denominator sin space A end fraction times cos space A minus sin space A times fraction numerator 1 over denominator cos space A end fraction plus sin space A space cos space A end cell row blank equals cell fraction numerator 1 over denominator sin space A space cos space A end fraction minus fraction numerator cos space A over denominator sin space A end fraction minus fraction numerator sin space A over denominator cos space A end fraction plus sin space A space cos space A end cell row blank equals cell fraction numerator 1 minus cos squared A minus sin squared A plus open parentheses sin space A space cos space A close parentheses squared over denominator sin space A space cos space A end fraction end cell row blank equals cell fraction numerator 1 minus 1 plus open parentheses sin space A space cos space A close parentheses squared over denominator sin space A space cos space A end fraction end cell row blank equals cell sin space A space cos space A end cell end table end style$

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