Svar:
#sin (a + b) = 56/65 #
Forklaring:
Givet, # tana = 4/3 og cotb = 5/12 #
# Rarrcota = 3/4 for #
# Rarrsina = 1 / CSCA = 1 / sqrt (1 + barneseng ^ 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 + barneseng ^ 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#
Svar:
#sin (a + b) = 56/65 #
Forklaring:
Her, # 0 ^ cirk <farve (violet) (a) <90 ^ circ => I ^ (st) Kvadrant => farve (blå) (Alle, fns> 0. #
# 0 ^ cirk <farve (violet) (b) <90 ^ circ => I ^ (st) Kvadrant => farve (blå) (Alle, fns.> 0 #
Så, # 0 ^ cirk <farve (violet) (a + b) <180 ^ cirk => I ^ (st) og II ^ (nd) kvadrant #
# => farve (blå) (sin (a + b)> 0 #
Nu, # Tana = 4/3 => seca = + sqrt (1 + tan ^ 2a) = sqrt (1 + 16/9) = 5/3 #
#:. farve (rød) (cosa) = 1 / seca = farve (rød) (3/5 #
# => Farve (rød) (sina) = + sqrt (1-cos ^ 2a) = sqrt (1-9 / 25) = farve (rød) (4/5 #
Også, # Cotb = 5/12 => cscb = + sqrt (1 + barneseng ^ 2b) = sqrt (1 + 25/144) = 13/12 #
#:. farve (rød) (sinb) = 1 / cscb = farve (rød) (12/13 #
# => Farve (rød) (cosb) = + sqrt (1-sin ^ 2b) = sqrt (1-144 / 169) = farve (rød) (5/13 #
derfor
#sin (a + b) = sinacosb + cosasinb #
# => Sin (a + b) = 4 / 5xx5 / 13 + 3 / 5xx12 / 13 #
#sin (a + b) = 20/65 + 36/65 = 56/65 #
