Jika A + B + C = pi maka buktikan bahwa sinA + sinB + sinC = 4cos(A/2) * cos(B/2) * cos(C/2)?

Kita harus membuktikan sinA+sinB+sinC=4cos(A/2)*cos(B/2)*cos(C/2)

Larutan

Mari kita mulai dengan LHS

sinA+sinB+sinC
= 2sin (A+B)/2cos(AB)/2+sin C
=2sin(pi-C)/2cos(AB)/2+2sin C/2cosC/2
=2cosC/2(cos( AB)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2

= RHS

Maka Terbukti

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