Cos2A = sqrt (2) (cosA-sinA) oplossen?

Antwoord:

Zie het antwoord hieronder …

Uitleg:

# Cos2A = sqrt2 (cosa-sina) #

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

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

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

# => (COSA + Sina) = sqrt2 #

# => ^ Sin 2A + cos ^ 2A + 2sinAcosA = 2 #vierkant aan beide kanten

# => 1 + sin2A = 2 #

# => Sin2A = 1 = sin90 ^ @ #

# => 2A = 90 ^ @ #

# => A = 45 ^ @ #

HOOP HET ANTWOORD HELPT …

DANK JE…

# Cos2A = sqrt2 (cosa-sina) #

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

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

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

Wanneer

# Cosa + Sina = 0 #

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

# => A = npi + pi / 4 "waar" n in 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 "waar" m in ZZ #