Paano patunayan ang kasalanan (theta + phi) / cos (theta-phi) = (tantheta + tanphi) / (1 + tanthetatanphi)?

Sagot:

Mangyaring tingnan ang patunay sa ibaba

Paliwanag:

Kailangan namin

#sin (a + b) = sinacosb + sinbcosa #

#cos (a-b) = cosacosb + sinasinb #

Samakatuwid, # LHS = sin (theta + phi) / cos (theta-phi) #

# = (sinthetacosphi + costhetasinphi) / (costhetacosphi + sinthetasinphi) #

Pagbabahagi ng lahat ng mga tuntunin sa pamamagitan ng# costhetacosphi #

(costhetacosphi) / (costhetacosphi) + (sinthetasinphi) / (costhetacosphi)) #

# = (sintheta / costheta + sinphi / cosphi) / (1 + sintheta / costheta * sinphi / cosphi) #

# = (tantheta + tanphi) / (1 + tanthetatanphi) #

# = RHS #

# QED #

Sagot:

Tingnan ang Paliwanag

Paliwanag:

Hayaan

# y = sin (theta + phi) / cos (theta-phi) #

# y = (sinthetacosphi + costhetasinphi) / (costhetacosphi + sinthetasinphi) #

Pagbabahagi ng #cos theta #, # y = (tanthetacosphi + sinphi) / (cosphi + tanthetasinphi) #

Pagbabahagi ng # cosphi #, # y = (tantheta + tanphi) / (1 + tanthetatanphi) #

kaya pinatunayan.

Sagot:

# "tingnan ang paliwanag" #

Paliwanag:

# "gamit ang" kulay (bughaw) "trigonometriko identities" #

# • kulay (puti) (x) kasalanan (x + y) = sinxcosy + cosxsiny #

# • kulay (puti) (x) cos (x-y) = cosxcosy + sinxsiny #

# "isaalang-alang ang kaliwang bahagi" #

# = (sinthetacosphi + costhetasinphi) / (costhetacosphi + sinthetasinphi) #

# "hatiin ang mga termino sa tagabilang / denominador sa pamamagitan ng" costhetacosphi #

# "at kanselahin ang karaniwang mga kadahilanan" #

# ((sinthetacosphi) / (costhetacosphi) + (costhetasinphi) / (costhetacosphi)) / ((costhetacosphi) / (costhetacosphi) + (sinthetasinphi) / (costhetacosphi)) = ((sintheta) / costheta + sinphi / cosphi) / (1 + sintheta / costhetaxxsinphi / cosphi #

# = (tantheta + tanphi) / (1 + tanthetatanphi) #

# = "kanang bahagi" rArr "napatunayan" #