Pertanyaan

Buktikanlah bahwa: a. sec 2 A + tan 2 A = cos A − sin A cos A + sin A

Buktikanlah bahwa:

a. $sec 2 A + tan 2 A = \frac{cos A + sin A}{cos A - sin A}$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $sec space 2 A plus space tan space 2 A equals fraction numerator cos space A plus sin space A over denominator cos space A minus sin space A end fraction$ .

Pembahasan

Ingat: Berdasarkan rumus-rumus di atas, maka Jadi, terbukti bahwa .

Ingat:

$rightwards double arrow sec space 2 A equals fraction numerator 1 over denominator cos space 2 A end fraction rightwards double arrow tan space 2 A equals fraction numerator sin space 2 A over denominator cos space 2 A end fraction rightwards double arrow cos space 2 A equals cos squared space A minus space sin squared space A rightwards double arrow sin space 2 A equals 2 space sin space A space cos space A rightwards double arrow sin squared space A plus cos squared space A equals 1 space$

Berdasarkan rumus-rumus di atas, maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell sec space 2 A plus space tan space 2 A end cell equals cell fraction numerator 1 over denominator cos space 2 A end fraction plus fraction numerator sin space 2 A over denominator cos space 2 A end fraction end cell row blank equals cell fraction numerator 1 plus sin space 2 A over denominator cos space 2 A end fraction end cell row blank equals cell fraction numerator sin squared space A plus cos squared space A plus 2 space sin space A space cos space A over denominator cos squared space A minus sin squared space A end fraction end cell row blank equals cell fraction numerator open parentheses sin space A plus cos space A close parentheses squared over denominator open parentheses cos space A plus sin space A close parentheses open parentheses cos space A minus sin space A close parentheses end fraction end cell row blank equals cell fraction numerator cos space A plus sin space A over denominator cos space A minus sin space A end fraction end cell end table$

Jadi, terbukti bahwa $sec space 2 A plus space tan space 2 A equals fraction numerator cos space A plus sin space A over denominator cos space A minus sin space A end fraction$ .