Ce este cos (arctan (3)) + păcat (arctan (4)) egal?

Răspuns:

#cos (arctan (3)) + sin (arctan (4)) = 1 / sqrt (10) + 4 / sqrt (17) #

Explicaţie:

Lăsa # Tan ^ -1 (3) = x #

atunci # Rarrtanx = 3 #

# Rarrsecx = sqrt (1 + tan ^ 2x) = sqrt (1 + 3 ^ 2) = sqrt (10) #

# Rarrcosx = 1 / sqrt (10) #

# Rarrx = cos ^ (- 1) (1 / sqrt (10)) = tan ^ (- 1) (3) #

De asemenea, să lăsați #tan ^ (- 1) (4) = y #

atunci # Rarrtany = 4 #

# Rarrcoty = 1 / # 4

# Rarrcscy = sqrt (1 + cot ^ 2y) = sqrt (1+ (1/4) ^ 2) = sqrt (17) / 4 #

# Rarrsiny = 4 / sqrt (17) #

# Rarry = sin ^ (- 1) (4 / sqrt (17)) = tan ^ (- 1) 4 #

Acum, #rarrcos (tan ^ (- 1) (3)) + sin (tan ^ (- 1) tan (4)) #

#rarrcos (cos ^ -1 (1 / sqrt (10))) + sin (sin ^ (- 1) (4 / sqrt (17))) = 1 / sqrt (10) + 4 / sqrt (17) #