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 $fraction numerator sin space alpha plus tan space alpha over denominator cos space alpha minus cotan space alpha end fraction$ sama dengan ...

Pembahasan Soal:

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

$m i equals 5 s a equals 3$

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

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space alpha plus tan space alpha over denominator cos space alpha minus cotan space alpha end fraction end cell equals cell fraction numerator begin display style fraction numerator d e over denominator m i end fraction end style plus begin display style fraction numerator d e over denominator s a end fraction end style over denominator begin display style fraction numerator s a over denominator m i end fraction end style minus begin display style fraction numerator s a over denominator d e end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 4 over 5 end style plus begin display style 4 over 3 end style over denominator begin display style 3 over 5 end style minus begin display style 3 over 4 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 12 plus 20 over denominator 15 end fraction end style over denominator begin display style fraction numerator 12 minus 15 over denominator 20 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 32 over 15 end style over denominator begin display style fraction numerator negative 3 over denominator 20 end fraction end style end fraction end cell row blank equals cell 32 over 15 cross times fraction numerator 20 over denominator negative 3 end fraction end cell row blank equals cell negative 640 over 45 end cell row blank equals cell negative 128 over 9 end cell row blank equals cell negative 14 2 over 9 end cell end table$

Jadi, nilai dari $fraction numerator sin space alpha plus tan space alpha over denominator cos space alpha minus cotan space alpha end fraction$ adalah $negative 14 2 over 9$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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