Pertanyaan

Buktikan tan ( a + 45 ) ∘ = cos a ∘ − sin a ∘ cos a ∘ + sin a ∘ .

Buktikan $tan (a + 45)^{\circ} = \frac{cos a ^{\circ} + sin a ^{\circ}}{cos a ^{\circ} - sin a ^{\circ}}$ . $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $tan space open parentheses a plus 45 close parentheses degree equals fraction numerator cos space a degree plus sin space a degree over denominator cos space a degree minus sin space a degree end fraction$ .

Pembahasan

Ingat! JumlahDua Sudut pada Tangen Akan dibuktikan . Bukti: Jadi, terbukti bahwa .

Ingat!

$tan space alpha equals fraction numerator sin space alpha over denominator cos space alpha end fraction$

Jumlah Dua Sudut pada Tangen

$tan space open parentheses alpha plus beta close parentheses equals fraction numerator tan space alpha plus tan space beta over denominator 1 minus tan space alpha times tan space beta end fraction$

Akan dibuktikan $tan space open parentheses a plus 45 close parentheses degree equals fraction numerator cos space a degree plus sin space a degree over denominator cos space a degree minus sin space a degree end fraction$ .

Bukti:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses a plus 45 close parentheses degree end cell equals cell fraction numerator tan space a degree plus tan space 45 degree over denominator 1 minus tan space a degree times tan space 45 degree end fraction end cell row blank equals cell fraction numerator tan space a degree plus 1 over denominator 1 minus tan space a degree times 1 end fraction end cell row blank equals cell fraction numerator 1 plus tan space a degree over denominator 1 minus tan space a degree end fraction end cell row blank equals cell fraction numerator 1 plus begin display style fraction numerator sin space a degree over denominator cos space a degree end fraction end style over denominator 1 minus fraction numerator sin space a degree over denominator cos space a degree end fraction end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator cos space a degree plus sin space a degree over denominator up diagonal strike cos space a degree end strike end fraction end style over denominator fraction numerator cos space a degree minus sin space a degree over denominator up diagonal strike cos space a degree end strike end fraction end fraction end cell row blank equals cell fraction numerator cos space a degree plus sin space a degree over denominator cos space a degree minus sin space a degree end fraction end cell end table$

Jadi, terbukti bahwa $tan space open parentheses a plus 45 close parentheses degree equals fraction numerator cos space a degree plus sin space a degree over denominator cos space a degree minus sin space a degree end fraction$ .

Latihan Bab

Konsep Kilat

Jumlah dan Selisih Dua Sudut

Sudut Rangkap dan Sudut Paruh

Perkalian Trigonometri