Kako preverite identiteto sec ^ 2 (x / 2) = (2secx + 2) / (secx + 2 + cosx)?

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

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

Zapomni si to # secx = 1 / cosx #

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

Zdaj, pomnožite vrh in dno # cosx #

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

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

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

# => 2 / (1 + cosx) #

Prikličite identiteto: # cos2x = 2cos ^ 2x-1 #

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

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

# => "Desna stran" = 2 / (2cos ^ 2 (x / 2)) = 1 / cos ^ 2 (x / 2) = barva (modra) (sec ^ 2 (x / 2)) = "levo Ročna stran "#

Kot zahteva

Kako preverite naslednjo identiteto?

Uporabite nekaj identitet in veliko poenostavitve. Glej spodaj. Pri obravnavi stvari, kot je cos3x, pomaga poenostaviti trigonometrične funkcije enote x; t.j. kot cosx ali cos ^ 3x. Lahko uporabimo pravilo vsote za kosinus, da bi to dosegli: cos (alfa + beta) = cosalphacosbeta-sinalphasinbeta Torej, ker cos3x = cos (2x + x), imamo: cos (2x + x) = cos2xcosx-sin2xsinx = (cos2xcosx-sin2xsinx = (cos) ^ 2x-sin ^ 2x) (cosx) - (2sinxcosx) (sinx) Zdaj lahko nadomestimo cos3x z zgornjim izrazom: (cos3x) / cosx = 1-4sin ^ 2x ((cos ^ 2x-sin ^ 2x) (cosx) ) - (2sinxcosx) (sinx)) / cosx = 1-4sin ^ 2x Ta večji del lahko razdelimo na dve

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