Sagot:
#sin (a + b) = 56/65 #
Paliwanag:
Given, # tana = 4/3 at 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 #
Ngayon, #sin (a + b) = sina * cosb + cosa * sinb #
#=(4/5)(5/13)+(3/5)*(12/13)=56/65#
Sagot:
#sin (a + b) = 56/65 #
Paliwanag:
Dito, # 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 => color (blue) (All, fns.> 0 #
Kaya, # 0 ^ circ <color (violet) (a + b) <180 ^ circ => I ^ (st) at II ^ (nd) Quadrant #
# => kulay (asul) (kasalanan (a + b)> 0 #
Ngayon, # tana = 4/3 => seca = + sqrt (1 + tan ^ 2a) = sqrt (1 + 16/9) = 5/3 #
#:. color (pula) (cosa) = 1 / seca = kulay (pula) (3/5 #
# => kulay (pula) (sina) = + sqrt (1-cos ^ 2a) = sqrt (1-9 / 25) = kulay (pula)
Gayundin, # cotb = 5/12 => cscb = + sqrt (1 + cot ^ 2b) = sqrt (1 + 25/144) = 13/12 #
#:. color (pula) (sinb) = 1 / cscb = kulay (pula) (12/13 #
# => kulay (pula) (cosb) = + sqrt (1-sin ^ 2b) = sqrt (1-144 / 169) = kulay (pula) (5/13 #
Kaya, #sin (a + b) = sinacosb + cosasinb #
# => sin (a + b) = 4 / 5xx5 / 13 + 3 / 5xx12 / 13 #
#sin (a + b) = 20/65 + 36/65 = 56/65 #
