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Jika  sudut lancip dan , nilai dari  sama dengan ...

Pertanyaan

Jika alpha sudut lancip dan s e c space alpha equals 5 over 3, nilai dari fraction numerator tan space alpha minus cotan space alpha over denominator tan space alpha plus cotan space alpha end fraction sama dengan ...

  1. 7 over 25 

  2. 7 over 24 

  3. negative 7 over 25 

  4. 1 over 26 

  5. fraction numerator negative 7 over denominator 24 end fraction 

Pembahasan Soal:

Diketahui s e c space alpha equals 5 over 3 sudut lancip di alpha.

m i equals 5 s a equals 3 

table attributes columnalign right center left columnspacing 0px end attributes row cell d e end cell equals cell square root of m i squared minus s a squared end root end cell row blank equals cell square root of 5 squared minus 3 cubed end root end cell row blank equals cell square root of 25 minus 9 end root end cell row blank equals cell square root of 16 end cell row blank equals 4 end table 

Nilai dari fraction numerator tan space alpha minus cotan space alpha over denominator tan space alpha plus cotan space alpha end fraction:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space alpha minus cotan space alpha over denominator tan space alpha plus cotan space alpha end fraction end cell equals cell fraction numerator begin display style fraction numerator d e over denominator s a end fraction end style minus begin display style fraction numerator s a over denominator d e end fraction end style over denominator begin display style fraction numerator d e over denominator s a end fraction end style plus begin display style fraction numerator s a over denominator d e end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 4 over 3 end style minus begin display style 3 over 4 end style over denominator begin display style 4 over 3 end style plus begin display style 3 over 4 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 16 minus 9 over denominator 12 end fraction end style over denominator begin display style fraction numerator 16 plus 9 over denominator 12 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 7 over 12 end style over denominator begin display style 25 over 12 end style end fraction end cell row blank equals cell 7 over 12 cross times 12 over 25 end cell row blank equals cell 7 over 25 end cell end table 

Sehingga, nilai dari fraction numerator tan space alpha minus cotan space alpha over denominator tan space alpha plus cotan space alpha end fraction adalah 7 over 25.

Jadi, jawwaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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