Question

Question #f29c8

Answer 1

`y = pi+4kpi, k = 0,1,2,cdots`

Explanation:

`tan(a+b)=(tan a+tanb)/(1-tan a tanb)`

so calling

`y/4 = 2arctan(1/3)+arctan(1/7)` then

`tan(y/4)=tan(2arctan(1/3)+arctan(1/7))=(3/4+1/7)/(1-3/4 1/7)=1`

so

`tan(y/4)=tan(pi/4+kpi)` then

`y = pi+4kpi, k = 0,1,2,cdots`

Answer 2

`180^@`

Explanation:

Use calculator.
`arctan (1/3) = 18^@43`
`2arctan (1/3) = 36^@87`
`arctan (1/7) = 8^@13`
`2arctan (1/3) + arctan (1/7) = 36.87 + 8.13 = 45^@`
Finally,
`4(2arctan (1/3) + arctan (1/7)) = 4 (45^@) = 180^@`