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Hitung nilai dari: 2 sin 6 0 ∘ ⋅ cos 3 0 ∘ sin 4 5 ∘ ⋅ cos 13 5 ∘ + tan 2 12 0 ∘ ​

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S. Nur

Master Teacher

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Ingat dan . Jadi

Ingat begin mathsize 14px style cos space open parentheses 180 to the power of ring operator minus x close parentheses equals negative cos space x end style dan begin mathsize 14px style tan space left parenthesis 180 to the power of ring operator minus x right parenthesis equals negative tan space x end style.

Jadi

begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree plus tan squared 120 degree over denominator 2 space sin space 60 degree times cos space 30 degree end fraction equals fraction numerator begin display style open parentheses 1 half square root of 2 close parentheses times cos space left parenthesis 180 to the power of ring operator minus 45 to the power of ring operator right parenthesis plus tan squared left parenthesis 180 to the power of ring operator minus 60 to the power of ring operator right parenthesis end style over denominator 2 times begin display style open parentheses 1 half square root of 3 close parentheses end style times begin display style left parenthesis 1 half square root of 3 right parenthesis end style end fraction equals fraction numerator begin display style open parentheses 1 half square root of 2 close parentheses times left parenthesis negative cos space 45 to the power of ring operator right parenthesis plus left parenthesis negative tan space 60 to the power of ring operator right parenthesis squared end style over denominator begin display style 3 over 2 end style end fraction equals open parentheses open parentheses 1 half square root of 2 close parentheses times open parentheses negative 1 half square root of 2 close parentheses plus open parentheses negative square root of 3 close parentheses squared close parentheses cross times 2 over 3 equals open parentheses negative 1 half plus 3 close parentheses cross times 2 over 3 equals 5 over 2 cross times 2 over 3 equals 5 over 3 end style 

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