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Tentukan nilai dari !

Pertanyaan

Tentukan nilai dari begin mathsize 14px style fraction numerator tan squared space 30 degree space sin squared space 60 degree plus tan squared space 60 degree space cos squared space 30 degree over denominator sin space 30 degree space cos space 60 degree end fraction end style!

Pembahasan Soal:

Kita gunakan nilai trigonometri pada sudut-sudut istimewa.

begin mathsize 14px style fraction numerator tan squared space 30 degree space sin squared space 60 degree plus tan squared space 60 degree space cos squared space 30 degree over denominator sin space 30 degree space cos space 60 degree end fraction equals fraction numerator open parentheses begin display style 1 third end style square root of 3 close parentheses squared open parentheses begin display style 1 half end style square root of 3 close parentheses squared plus open parentheses square root of 3 close parentheses squared open parentheses begin display style 1 half end style square root of 3 close parentheses squared over denominator open parentheses begin display style 1 half end style close parentheses open parentheses begin display style 1 half end style close parentheses end fraction equals fraction numerator open parentheses begin display style 1 third end style close parentheses open parentheses begin display style 3 over 4 end style close parentheses plus open parentheses 3 close parentheses open parentheses begin display style 3 over 4 end style close parentheses over denominator begin display style 1 fourth end style end fraction equals fraction numerator begin display style 1 fourth end style plus begin display style 9 over 4 end style over denominator begin display style 1 fourth end style end fraction equals fraction numerator begin display style 10 over 4 end style over denominator begin display style 1 fourth end style end fraction equals 10 end style

Jadi, nilai dari begin mathsize 14px style fraction numerator tan squared space 30 degree space sin squared space 60 degree plus tan squared space 60 degree space cos squared space 30 degree over denominator sin space 30 degree space cos space 60 degree end fraction end style adalah begin mathsize 14px style 10 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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