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

Odgovor:

Z uporabo naslednjih pravil:

# secx = 1 / cosx #

# cscx = 1 / sinx #

# tanx = sinx / cosx #

Pojasnilo:

Potrebno je dokazati: # sec ^ 2x / tanx = secxcscx #

Izhajajoč iz Stran leve roke enačbe

# "LHS" = sek ^ 2x / tanx #

# = (secx) ^ 2 / tanx #

# = (1 / cosx) ^ 2 / (sinx / cosx) #

# = 1 / (cosx) ^ 2 ÷ (sinx / cosx) #

# = 1 / (cosx) ^ cancel2 * cancelcosx / sinx #

# = 1 / cosx * 1 / sinx #

# = barva (modra) (secxcscx #

# "QED" #

Kako preverite? Tan x + cos x = sin x (sec x + cotan x)

Glej spodaj. LHS = tanx + cosx = sinx / cosx + cosx = sinx (1 / cosx + cosx / sinx) = sinx (secx + cotx) = RHS

Kako preverite posteljico (x) / sin (x) -tan (x) / cos (x) = csc (x) sec (x) 1 / (sin (x) + cos (x))?

"To ni res, zato izpolnite x = 10 ° npr. In videli boste, da enakost ne drži." "Nič več dodati."

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