Selesaikan cos2A = sqrt (2) (cosA-sinA)?

Jawapan:

Lihat jawapan di bawah …

Penjelasan:

# cos2A = sqrt2 (cosA-sinA) #

# => cos2A (cosA + sinA) = sqrt2 (cos ^ 2A-sin ^ 2A) #

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

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

# => (cosA + sinA) = sqrt2 #

# => sin ^ 2A + cos ^ 2A + 2sinAcosA = 2 #menjimatkan kedua-dua belah pihak

# => 1 + sin2A = 2 #

# => sin2A = 1 = sin90 ^ @ #

# => 2A = 90 ^ @ #

# => A = 45 ^ @ #

HARAPAN JAWAB MELALUI …

TERIMA KASIH…

# 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 #

Bila

# cosA + sinA = 0 #

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

# => A = npi + pi / 4 "di mana" n dalam 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 "di mana" m dalam ZZ #