Kako provjeriti identitet sek ^ 2 (x / 2) = (2secx + 2) / (secx + 2 + cosx)?

Potrebno je dokazati: # sek ^ 2 (x / 2) = (2secx + 2) / (secx + 2 + cosx) #

# "Desna strana" = (2secx + 2) / (secx + 2 + cosx) #

Zapamti to # Secx = 1 / cosx #

# => (2 * 1 / cosx + 2) / (1 / cosx + 2 + cosx) #

Sada pomnožite vrh i dno # Cosx #

# => (cosx xx (2 * 1 / cosx + 2)) / (cosx xx (1 / cosx + 2 + cosx)) #

# => (2 + 2cosx) / (1 + 2cosx + cos ^ 2x) #

Faktorizirajte dno, # => (2 (1 + cosx)) / (1 + cosx) ^ 2 #

# => 2 / (1 + cosx) #

Sjetite se identiteta: # Cos2x = 2cos ^ 2x-1 #

# => 1 + cos2x = 2cos ^ 2x #

Slično: # 1 + cosx = 2cos ^ 2 (x / 2) *

# => "Desna strana" = 2 / (2cos ^ 2 (x / 2)) = 1 / cos ^ 2 (x / 2) = boja (plava) (sec ^ 2 (x / 2)) = "lijevo Hand Side "# #

Po potrebi

Kako provjeriti sek ^ 2 x / tan x = sec x csc x?

Koristeći sljedeća pravila: secx = 1 / cosx cscx = 1 / sinx tanx = sinx / cosx Potrebno je dokazati: sec ^ 2x / tanx = secxcscx Počevši od lijeve strane Jednadžba "LHS" = sec ^ 2x / tanx = (secx) ^ 2 / tanx = (1 / cosx) ^ 2 / (sinx / cosx) = 1 / (cosx) ^ 2 sin (sinx / cosx) = 1 / (cosx) ^ cancel2 * cancelcosx / sinx = 1 / cosx * 1 / sinx = boja (plava) (secxcscx "QED")

Kako provjeriti identitet sec ^ 4theta = 1 + 2tan ^ 2theta + tan ^ 4theta?

Dokaz ispod Prvo ćemo dokazati 1 + tan ^ 2theta = sec ^ 2theta: sin ^ 2theta + cos ^ 2theta = 1 sin ^ 2theta / cos ^ 2theta + cos ^ 2theta / cos ^ 2theta = 1 / cos ^ 2theta tan ^ 2theta + 1 = (1 / costheta) ^ 2 1 + tan ^ 2theta = sec ^ 2theta Sada možemo dokazati vaše pitanje: sec ^ 4theta = (sec ^ 2theta) ^ 2 = (1 + tan ^ 2theta) ^ 2 = 1 + 2tan ^ theta + tan ^ 4theta

Kako provjeriti identitet 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Vidi ispod 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta Desna strana = sec ^ 6theta-tan ^ 6theta = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3-> koristi razliku od dvije kocke formula = (sek ^ 2teta-tan ^ 2tea) (sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta) = 1 * (sec ^ 4theta + s ^ ^ 2thetatan ^ 2theta + tan ^ 4theta = sek ^ 2tea sek ^ 2 theta + sec ^ 2tetatan ^ 2theta + tan ^ 2teta tan ^ 2 theta = sek ^ 2tea (tan ^ 2theta + 1) + sec ^ 2thetatan ^ 2theta + tan ^ 2 theta (sec ^ 2theta-1) = sek ^ 2tetatan ^ 2 theta + sec ^ 2theta + sec ^ 2tetatan ^ 2theta + sec ^ 2tetatan ^ 2teta-tan ^ 2theta = sek ^ 2t