Pertanyaan

Nilai dari: sin 27 0 ∘ + cos 18 0 ∘ tan 12 0 ∘ − sin 33 0 ∘ + cos 24 0 ∘ − ctg 15 0 ∘

Nilai dari:

$\frac{tan 12 0 ^{\circ} - sin 33 0 ^{\circ} + cos 24 0 ^{\circ} - ctg 15 0 ^{\circ}}{sin 27 0 ^{\circ} + cos 18 0 ^{\circ}}$

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator tan space 120 degree minus sin space 330 degree plus cos space 240 degree minus ctg space 150 degree over denominator sin space 270 degree plus cos space 180 degree end fraction end cell row blank equals cell fraction numerator tan space open parentheses 90 degree plus 30 degree close parentheses minus sin space open parentheses 270 degree plus 60 degree close parentheses plus cos space open parentheses 270 degree minus 30 degree close parentheses minus begin display style fraction numerator 1 over denominator tan space left parenthesis 90 degree plus 60 degree right parenthesis end fraction end style over denominator sin space 270 degree plus cos space 180 degree end fraction end cell row blank equals cell fraction numerator negative tan space 30 degree minus open parentheses negative cos space 60 degree close parentheses plus open parentheses negative sin space 30 degree close parentheses minus begin display style fraction numerator 1 over denominator negative tan space 60 degree space end fraction end style over denominator sin space 270 degree plus cos space 180 degree end fraction end cell row blank equals cell fraction numerator negative tan space 30 degree plus cos space 60 degree minus sin space 30 degree plus begin display style fraction numerator 1 over denominator tan space 60 degree space end fraction end style over denominator sin space 270 degree plus cos space 180 degree end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator square root of 3 over denominator 3 end fraction end style plus begin display style 1 half end style minus begin display style 1 half end style plus begin display style fraction numerator 1 over denominator square root of 3 space end fraction end style over denominator negative 1 plus open parentheses negative 1 close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator square root of 3 over denominator 3 end fraction end style plus begin display style fraction numerator square root of 3 over denominator 3 space end fraction end style over denominator negative 2 end fraction end cell row blank equals cell fraction numerator 0 over denominator negative 2 end fraction end cell row blank equals 0 end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator tan space 120 degree minus sin space 330 degree plus cos space 240 degree minus ctg space 150 degree over denominator sin space 270 degree plus cos space 180 degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table end style$ .