Question

Prove that

2tan^-1 1/2 + tan^-1 1/7 = tan^-1 31/17

Answer 1

@sleepyhead314

Answer 2

Sorry, I really don't know how to do this :/
hopefully @jdoe0001 @zepdrix @phi @shamim can help?

Answer 3

I went through my book a bit,

You gotta use tan^-1 x + tan^-1 y as tan^-1 x+y/1 + xy

So its 2(1/2) + 1/7/1 + 1/2 x 1/7

1 + 1/7 / 1 + 1/14

Or

8/7/15/14

cancel cancel..

16/15

tan^-1 16/15

Someone see if this is correct? :(

Answer 4

@sleepyhead314 its okay <3

Answer 5

http://www.rapidtables.com/math/trigonometry/arctan.htm

Answer 6

darn, its wrong.

Its given in the question that its 2tan^-1 1/2 + tan^-1 1/7

So it means I gotta first get this in the form of tan^-1 x + tan^-1 y

The 2tan^-1 x will be solved using 2x/1-x^2

that is

2 x 1/2 / 1 - (1/2)^2

= 4/3

so its 4/3 + 1/7 / 1 - 4/3 x 1/7

28 + 3/21 / 1 - 4/21

31/21 / 17/21

31/21 x 21/17

cancel cancel and 31/17

tan^-1 31/17 = tan^-1 31/17

Thus proved

Answer 7

thank you! (: