Tan ( cos ^ {- 1} frac {3} {5} + tan ^ {- 1} frac {1} {4})의 값은 얼마입니까?

대답:

(1) (cos ^ (- 1) (3/5) + tan ^ (-1) (1/4)) = 19 / 8 #

설명:

방해 #cos ^ (- 1) (3/5) = x # 그때

# rarrsecx = 5 / 3 #

# rarrtanx = sqrt (sec ^ 2x-1) = sqrt ((5/3) ^ 2-1) = sqrt ((5 ^ 2-3 ^ 2) / 3 ^ 2) = 4 / 3 #

# rarrx = tan ^ (-1) (4/3) = cos ^ (- 1) (3/5) #

자, (A + B) / (1-AB)) # tan ^ (-1) (A) + tan ^ (-1) (B) = tan ^

(1) (cos ^ (- 1) (3/5) + tan ^ (- 1) (1/4)) #

(tan ^ (- 1) (4/3) + tan ^ (- 1) (1/4)) #

(4/3 + 1 / 4) / (1- (4/3) * (1/4)))) # = tan ^ (- 1)

#=(19/12)/(8/12)=19/8#