Pertanyaan

Jawablah dengan jelas dan benar. Jika sin α = 17 8 dan cos β = 5 3 , untuk α dan β sudut lancip, tentukannilai dari: 1 − tan α tan β tan α + tan β

Jawablah dengan jelas dan benar.

Jika $sin α = \frac{8}{17}$ dan $cos β = \frac{3}{5}$ , untuk $α$ dan $β$ sudut lancip, tentukan nilai dari:

$\frac{tan α + tan β}{1 - tan α tan β}$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

dan sudut lancip, maka berada di kuadran I. Maka,

dan sudut lancip, maka berada di kuadran I.

begin mathsize 14px style sin space alpha space equals space 8 over 17 space rightwards double arrow space tan space alpha space equals space 8 over 15 cos space beta space equals space 3 over 5 space rightwards double arrow space tan space beta space equals space 4 over 3 end style

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space alpha space plus space tan space beta over denominator 1 space minus space tan space alpha space tan space beta end fraction space end cell equals cell space fraction numerator begin display style 8 over 15 end style space plus space begin display style 4 over 5 end style over denominator 1 space minus space open parentheses begin display style 8 over 15 end style space cross times space begin display style 4 over 5 end style close parentheses end fraction end cell row blank equals cell space fraction numerator begin display style fraction numerator 8 space minus space 12 over denominator 15 end fraction end style over denominator 1 space minus space begin display style 32 over 74 end style end fraction end cell row blank equals cell space fraction numerator negative begin display style 4 over 15 end style over denominator begin display style fraction numerator 74 space minus space 32 over denominator 74 end fraction end style end fraction end cell row blank equals cell space fraction numerator negative begin display style 4 over 15 end style over denominator begin display style 42 over 74 end style end fraction end cell row blank equals cell space minus 4 over 15 space cross times space 42 over 74 end cell row blank equals cell space minus 168 over 1110 end cell row blank equals cell space minus space 84 over 555 end cell end table end style$