Kako dokazati to identiteto? sin ^ 2x + tan ^ 2x * sin ^ 2x = tan ^ 2x

Odgovor:

Prikazano spodaj…

Pojasnilo:

Uporabi naše identitete trigonometrov …

# sin ^ 2 x + cos ^ 2 x = 1 #

# => sin ^ 2 x / cos ^ 2 x + cos ^ 2 x / cos ^ 2 x = 1 / cos ^ 2 x #

# => tan ^ 2 x + 1 = 1 / cos ^ 2 x #

Faktor leve strani vaše težave …

# => sin ^ 2 x (1 + tan ^ 2 x) #

# => sin ^ 2 x (1 / cos ^ 2 x) = sin ^ 2 x / cos ^ 2 x #

# => (sinx / cosx) ^ 2 = tan ^ 2 x #

Glede, # sin ^ 2 x + tan ^ 2x sin ^ 2x #

# = sin ^ 2 x (1 + tan ^ 2 x) #

# = sin ^ 2 x sek ^ 2x # (kot,# sek ^ 2x - tan ^ 2 x = 1) #

# = sin ^ 2x (1 / (cos ^ 2x)) #

# = tan ^ 2 x #

Dokazano

Kako dokazati (1 + sinx-cosx) / (1 + cosx + sinx) = tan (x / 2)?

Glej spodaj. LHS = (1-cosx + sinx) / (1 + cosx + sinx) = (2sin ^ 2 (x / 2) + 2sin (x / 2) * cos (x / 2)) / (2cos ^ 2 (x / 2) + 2sin (x / 2) * cos (x / 2) = (2sin (x / 2) [sin (x / 2) + cos (x / 2)]) / (2cos (x / 2) * [ sin (x / 2) + cos (x / 2)]) = tan (x / 2) = RHS

Kako preverite identiteto sec ^ 4theta = 1 + 2tan ^ 2theta + tan ^ 4theta?

Dokaz spodaj Najprej bomo dokazali 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 Zdaj lahko dokažemo vaše vprašanje: sec ^ 4theta = (sec ^ 2theta) ^ 2 = (1 + tan ^ 2theta) ^ 2 = 1 + 2tan ^ theta + tan ^ 4theta

Kako preverite identiteto 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Glej spodaj 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta desna stran = sec ^ 6theta-tan ^ 6theta = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3-> uporabi razliko dveh kock formula = (sec ^ 2teta-tan ^ 2theta) (sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta) = 1 * (sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta) = sec ^ 4theta + sec ^ 2thetatan ^ 2theta + tan ^ 4theta = sek ^ 2tea sek ^ 2 theta + sec ^ 2tetatan ^ 2theta + tan ^ 2theta tan ^ 2 theta = sek ^ 2tea (tan ^ 2theta + 1) + sec ^ 2thetatan ^ 2theta + tan ^ 2theta (sec ^ 2theta-1) = sec ^ 2tetatan ^ 2theta + sec ^ 2theta + sec ^ 2tetatan ^ 2