Question

Question #4abc6

Answer 1

Prove arctan (1/3) + arctan (1/2)(1/7) = pi/8

Explanation:

tan x = 1/3 --> arc `x = 18^@43`
`1/2tan y = (0. 14)/2 = 0.07` --> arc `y = 4^@08`
`x + y = 22^@51`
`pi/8 = 180/8 = 22^@50.`
Therefor, the equation is proven.

Answer 2

Let `tan^-1 ( 1/3) =x` and `tan^-1 (1/7)= y`

It would be equivalent of the required proof, if it is proved that `2tan^-1 (1/3) + tan^-1 (1/7)= pi/4`
(
`tan^-1 (1/3) +tan^-1 (1/7)= tan^-1 ((1/3+1/7)/(1-(1/3)(1/7)))` =`tan^-1 (1/2)`

Again `tan^-1 (1/3) +tan^-1 (1/2) = tan^-1 ((1/3+1/2)/(1- (1/2)(1/3)))` = `tan^-1 1` = `pi/4`