Hvordan verificerer du identiteten tanthetacsc ^ 2theta-tantheta = cottheta?

Svar:

Bevis nedenfor

Forklaring:

#tantheta * csc ^ 2theta - tantheta #

# = sintheta / costheta * (1 / sintheta) ^ 2 - sintheta / costheta #

# = sintheta / costheta * 1 / sin ^ 2theta - sintheta / costheta #

# = 1 / (sinthetacostheta) - sintheta / costheta #

# = (1-sin ^ 2-theta) / (sinthetacostheta) #

# = Cos ^ 2-theta / (sinthetacostheta) #

# = Costheta / sintheta #

# = Cottheta #

Noter det # sin ^ 2theta + cos ^ 2theta = 1 #, derfor # cos ^ 2theta = 1- sin ^ 2theta #

# LHS = tantheta * csc ^ 2theta - tantheta #

# = tantheta (csc ^ 2theta - 1) #

# = tantheta (1 + cot ^ 2theta - 1) #

# = tantheta * barneseng ^ 2theta #

# = Cottheta = RHS #

Hvordan verificerer du identiteten sec ^ 2 (x / 2) = (2secx + 2) / (secx + 2 + cosx)?

Nødvendig at bevise: sec ^ 2 (x / 2) = (2sekx + 2) / (secx + 2 + cosx) "Højre side" = (2sek x + 2) / (sekx + 2 + cosx) Husk at secx = 1 / cosx => (2 * 1 / cosx + 2) / (1 / cosx + 2 + cosx) Nu multipliserer toppen og bunden ved cosx => (cosx xx (2 * 1 / cosx + 2)) / (cosx xx (1 + cosx + 2 + cosx)) => (2 + 2cosx) / (1 + 2cosx + cos ^ 2x) Faktoriser bunden, => (2 (1 + cosx)) / (1 + cosx) ^ 2 = > 2 / (1 + cosx) Genkald identiteten: cos2x = 2cos ^ 2x-1 => 1 + cos2x = 2cos ^ 2x Tilsvarende: 1 + cosx = 2cos ^ 2 (x / 2) => "Højre side" = 2 / (2cos ^ 2 (x / 2)) = 1 / cos ^ 2 (

Hvordan verificerer du identiteten sec ^ 4theta = 1 + 2tan ^ 2theta + tan ^ 4theta?

Bevis nedenunder Først vil vi bevise 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 Nu kan vi bevise dit spørgsmål: sec ^ 4theta = (sec ^ 2theta) ^ 2 = (1 + tan ^ 2theta) ^ 2 = 1 + 2tan ^ theta + tan ^ 4theta

Hvordan verificerer du identiteten 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta?

Se nedenfor 3sec ^ 2thetatan ^ 2theta + 1 = sec ^ 6theta-tan ^ 6theta Højre Side = sec ^ 6theta-tan ^ 6theta = (sec ^ 2theta) ^ 3- (tan ^ 2theta) ^ 3-> brug forskel på to terninger formel = (sec ^ 2theta-tan ^ 2theta) (sec ^ 4eeta + sec ^ 2tetatan ^ 2theta + tan ^ 4eeta) = 1 * (sec ^ 4eeta + sec ^ 2tetatan ^ 2ta + tan ^ 4eeta) = sec ^ 4theta + sek ^ 2thetatan ^ 2theta + tan ^ 4theta = sec ^ 2theta sec ^ 2 theta + sec ^ 2thetatan ^ 2theta + tan ^ 2theta tan ^ 2 theta = sec ^ 2theta (tan ^ 2theta + 1) + sec ^ 2thetatan ^ 2theta + tan ^ 2theta (sec ^ 2theta-1) = sec ^ 2tetatan ^ 2theta + sec ^ 2theta + sec ^ 2the