Riešiť cos2A = sqrt (2) (cosA-sinA)?

odpoveď:

Pozrite si odpoveď nižšie …

vysvetlenie:

# Cos2A = sqrt2 (cosa-Sina) #

# => Cos2A (cosa + sina) = sqrt2 (cos ^ 2A-sin ^ 2A) #

# => cos2A (cosA + sinA) = sqrt2 cdot cos2A #

# => Zrušiť (cos2A) (cosA + sinA) = sqrt2 cdot zrušiť (cos2A #

# => (Cosa + sina) = sqrt2 #

# => Sin ^ 2A + cos ^ 2A + 2sinAcosA = 2 #na druhú stranu

# => 1 + sin2 = 2 #

# => Sin2 = 1 = sin90 ^ @ #

# => 2A = 90 ^ @ #

# => A = 45 ^ @ #

HOPE ODPOVEĎ …

ĎAKUJEM…

# Cos2A = sqrt2 (cosa-Sina) #

# => Cos ^ 2A-sin ^ 2A-sqrt2 (cosa-sina) = 0 #

# => (Cosa-Sina) (cosa + Sina) -sqrt2 (cosa-sina) = 0 #

# => (Cosa-Sina) (cosa + SINA-sqrt2) = 0 #

Kedy

# Cosa + sina = 0 #

# => Tana = 1 = tan (pi / 4) #

# => A = npi + pi / 4 "kde" n v ZZ #

# Cosa + sina = sqrt2 #

# => 1 / sqrt2cosA + 1 / sqrt2sinA = 1 #

# => Cos (pi / 4) cosa + sin (pi / 4) Sina = 1 #

# => Cos (A-pi / 4) = 1 #

# => A = 2mpi + pi / 4 "kde" m v ZZ #