Antwoord:
#sin (a + b) = 56/65 #
Uitleg:
Gegeven, # tana = 4/3 en cotb = 5/12 #
# Rarrcota = 3/4 #
# Rarrsina = 1 / CSCA = 1 / sqrt (1 + kinderbed ^ 2a) = 1 / sqrt (1 + (3/4) ^ 2) = 4/5 #
# Rarrcosa = sqrt (1-sin ^ 2a) = sqrt (1- (4/5) ^ 2) = 3/5 #
# Rarrcotb = 5/12 #
# Rarrsinb = 1 / cscb = 1 / sqrt (1 + kinderbed ^ 2b) = 1 / sqrt (1+ (5/12) ^ 2) = 12/13 #
# Rarrcosb = sqrt (1-sin ^ 2b) = sqrt (1- (12/13) ^ 2) = 5/13 #
Nu, #sin (a + b) = sina * cosb cosa + * sinb #
#=(4/5)(5/13)+(3/5)*(12/13)=56/65#
Antwoord:
#sin (a + b) = 56/65 #
Uitleg:
Hier, # 0 ^ circ <color (violet) (a) <90 ^ circ => I ^ (st) Quadrant => color (blue) (All, fns.> 0. #
# 0 ^ circ <color (violet) (b) <90 ^ circ => I ^ (st) Quadrant => kleur (blauw) (Alles, fns.> 0 #
Zo, # 0 ^ circ <color (violet) (a + b) <180 ^ circ => I ^ (st) en II ^ (nd) Quadrant #
# => kleur (blauw) (sin (a + b)> 0 #
Nu, # Tana = 4/3 => seca = + sqrt (1 + tan ^ 2a) = sqrt (1 + 16/9) = 5/3 #
#:. kleur (rood) (cosa) = 1 / seca = (rood) (3/5 #
# => Kleur (rood) (sina) + = sqrt (1-cos ^ 2a) = sqrt (1-9 / 25) = (rood) (4/5 #
Ook, # Cotb = 12/05 => cscb = + sqrt (1 + kinderbed ^ 2b) = sqrt (1 + 25/144) = 13/12 #
#:. kleur (rood) (sinb) = 1 / cscb = (rood) (12/13 #
# => Kleur (rood) (cosb) + = sqrt (1-sin ^ 2b) = sqrt (1-144 / 169) = (rood) (13/05 #
Vandaar, #sin (a + b) = + sinacosb cosasinb #
# => Sin (a + b) = 4 / 5xx5 / 13 + 3 / 5xx12 / 13 #
#sin (a + b) = 20/65 + 36/65 = 56/65 #
