Hva er cos (arctan (3)) + synd (arctan (4)) lik?

Hva er cos (arctan (3)) + synd (arctan (4)) lik?
Anonim

Svar:

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

Forklaring:

La # Tan ^ -1 (3) = x #

deretter # Rarrtanx = 3 #

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

# Rarrcosx = 1 / sqrt (10) #

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

Også, la #tan ^ (- 1) (4) = y #

deretter # 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 #

Nå, #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) #