Çöz (2 + sqrt3) cos teta = 1-sin teta?

Cevap:

# Rarrx = (6n-1) * (p / 3) #

# Rarrx = (4n + 1) pi / 2 # Nerede # NrarrZ #

Açıklama:

#rarr (2 + sqrt (3)) cosx = 1-SiNx #

# Rarrtan75 ^ @ * cosx + SiNx = 1 #

#rarr (sin75 ^ @ * cosx) + SiNx = 1 # / (^ @ cos75)

# Rarrsinx * cos75 ^ + cosx * sin75 ^ @ = cos75 ^ @ = sin (90 ^ @ - 15 ^ @) = sin15 ^ @ #

#rarrsin (x + 75 ^ @) - sin15 ^ @ = 0 #

# Rarr2sin ((x + 75 ^ @ - 15 ^ @) / 2) cos ((x + 75 ^ + 15 ^ @) / 2) = 0 #

#rarrsin ((x + 60 ^ @) / 2) * cos ((x + 90 ^ @) / 2) = 0 #

ya #rarrsin ((x + 60 ^ @) / 2) = 0 #

#rarr (x + 60 ^ @) / 2 = NPI #

# Rarrx = 2npi-60 ^ @ = 2npi-pi / 3 = (6n-1) * (p / 3) #

veya, #cos ((x + 90 ^ @) / 2) = 0 #

#rarr (x + 90 ^ @) / 2 = (2n + 1) pi / 2 #

# Rarrx = 2 * (2n + 1) pi / 2-pi / 2 = (4-n + 1) pi / 2 #

Cevap:

Eğer, # Costheta = 0 => sintheta = 1 => = (4k + 1) pi / 2, Kinz # teta

# Teta = 2kpi-pi / 3, # Kinz,

Açıklama:

# (2 + SQRT3) costheta = 1-sintheta #

#andcostheta! = 0 #, iki tarafı da bölerek # Costheta #

# 2 + sqrt3 = sectheta-tantheta => sectheta-tantheta = 2 + sqrt3 ila (I) #

#:. 1 / (sectheta-tantheta) = 1 / (+ SQRT3 2) ## => (Sn ^ 2teta-kahve renkli ^ 2teta) / (sectheta-tantheta) = 1 / (+ SQRT3 2) * (2-SQRT3) / (2-SQRT3) #

# => sectheta + tantheta = 2-sqrt3 ila (II) #

Ekleme # (I) ve (II) #anlıyoruz.# 2sectheta = 4 => sectheta = 2 #

#color (kırmızı) (costheta = 1/2> 0) #, Verilen equn itibaren.

# Costheta = 1/2 => (+ SQRT3 2) (1/2) = 1-sintheta ## => 1 + SQRT (3) / 2 = 1-sintheta => renkli (kırmızı) (sintheta = -sqrt (3) / 2 <0) #

# Teta = 2kpi-pi / 3, # Kinz,………. # (IV ^ (th) #kadran)