Vastaus:
#sin (a + b) = 56/65 #
Selitys:
Ottaen huomioon, # tana = 4/3 ja cotb = 5/12 #
# Rarrcota = 3/4 #
# Rarrsina = 1 / CSCA = 1 / sqrt (1 + cot ^ 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 + cot ^ 2b) = 1 / sqrt (1 + (5/12) ^ 2) = 12/13 #
# Rarrcosb = sqrt (1-sin ^ 2b) = sqrt (1- (12/13) ^ 2) = 5/13 #
Nyt, #sin (a + b) = sina * cosb + cosa * sinb #
#=(4/5)(5/13)+(3/5)*(12/13)=56/65#
Vastaus:
#sin (a + b) = 56/65 #
Selitys:
Tässä, # 0 ^ circ <väri (violetti) (a) <90 ^ circ => I ^ (st) Quadrant => väri (sininen) (Kaikki, fns.> 0. #
# 0 ^ circ <väri (violetti) (b) <90 ^ circ => I ^ (st) Quadrant => väri (sininen) (Kaikki, fns.> 0 #
Niin, # 0 ^ circ <väri (violetti) (a + b) <180 ^ circ => I ^ (st) ja II ^ (nd) Quadrant #
# => väri (sininen) (sin (a + b)> 0 #
Nyt, # Tana = 4/3 => seca = + sqrt (1 + tan ^ 2a) = sqrt (1 + 16/9) = 5/3 #
#:. väri (punainen) (cosa) = 1 / seca = väri (punainen) (3/5 #
# => Väri (punainen) (sina) = + sqrt (1-cos ^ 2a) = sqrt (1-9 / 25) = väri (punainen) (4/5 #
Myös, # CoTb = 5/12 => CSCB = + sqrt (1 + cot ^ 2b) = sqrt (1 + 25/144) = 13/12 #
#:. väri (punainen) (sinb) = 1 / CSCB = väri (punainen) (12/13 #
# => Väri (punainen) (cosb) = + sqrt (1-sin ^ 2b) = sqrt (1-144 / 169) = väri (punainen) (5/13 #
Siten, #sin (a + b) = sinacosb + cosasinb #
# => Sin (a + b) = 4 / 5xx5 / 13 + 3 / 5xx12 / 13 #
#sin (a + b) = 20/65 + 36/65 = 56/65 #
