Odgovor:
Pokaži
Pojasnilo:
Odgovor:
Oglejte si spodnji dokaz
Pojasnilo:
Potrebujemo
Zato,
Odgovor:
Vljudno našli a Dokaz v Razlaga.
Pojasnilo:
Uporabili bomo Identiteta:
Dokaži, da (1 + secx) / tanx = posteljica (x / 2)?
LHS = (1 + secx) / tanx = (1 + 1 / cosx) / tanx = ((1 + cosx) / preklic (cosx)) / (sinx / preklic (cosx)) = (1 + cosx) / sinx = (2cos ^ 2 (x / 2)) / (2sin (x / 2) * cos (x / 2)) = posteljica (x / 2) = RHS
Dokaži, da je cosec (x / 4) + cosec (x / 2) + cosecx = posteljica (x / 8) -cotx?
LHS = cosec (x / 4) + cosec (x / 2) + cosecx = cosec (x / 4) + cosec (x / 2) + cosecx + cotx-cotx = cosec (x / 4) + cosec (x / 2) ) + barva (modra) [1 / sinx + cosx / sinx] -cotx = cosec (x / 4) + cosec (x / 2) + barva (modra) [(1 + cosx) / sinx] -cotx = cosec ( x / 4) + cosec (x / 2) + barva (modra) [(2cos ^ 2 (x / 2)) / (2sin (x / 2) cos (x / 2))] - cotx = cosec (x / 4) + cosec (x / 2) + barva (modra) (cos (x / 2) / sin (x / 2)) - cotx = cosec (x / 4) + barva (zelena) (cosec (x / 2) + otroška posteljica (x / 2) - barva cotx (magenta) "Nadaljevanje na podoben način kot prej" = cosec (x / 4) + barvna (zelena) pos
Dokaži, da posteljica (A / 2) - 3cot ((3A) / 2) = (4sinA) / (1 + 2cosA)?
Glejte Razlago. Vemo, da je tan3theta = (3tantheta-tan ^ 3theta) / (1-3tan ^ 2theta). :. cot3theta = 1 / (tan3theta) = (1-3tan ^ 2theta) / (3tantheta-tan ^ 3theta): .cot ((3A) / 2) = {1-3tan ^ 2 (A / 2)} / {3tan ( A / 2) -tan ^ 3 (A / 2)}. Izpustitev tan (A / 2) = t, imamo, posteljica (A / 2) -3cot ((3A) / 2), = 1 / t-3 {(1-3t ^ 2) / (3t-t ^ 3) )}, 1 / - {3 (1-3t ^ 2)} / {t (3-t ^ 2)}, = {(3-t ^ 2) -3 (1-3t ^ 2)} / { t (3-t ^ 2)}, = (8t ^ odpoved (2)) / {preklic (t) (3-t ^ 2)}, = (8t) / {(1 + t ^ 2) +2 ( 1-t ^ 2)} = {4 * (2t) / (1 + t ^ 2)} / {(1 + t ^ 2) / (1 + t ^ 2) + 2 * (1-t ^ 2) / (1 + t ^ 2)}. Zapomnite si, da (2t)