The Purplemath Forums

by **mathnoob** on Wed Jul 29, 2009 5:59 pm

if x = 1/2 and (x + 1)(y + 1) = 2, find the radian measure of arctan (x) + arctan (y)

could someone help me get started please? :shock:

**Sponsor**

by **Honeysuckle588** on Wed Jul 29, 2009 7:25 pm

Perhaps you should start by determining the value of y.

by **mathnoob** on Wed Jul 29, 2009 8:19 pm

y = 1/3, but then what?

by **stapel_eliz** on Wed Jul 29, 2009 9:52 pm

You have arctangents. These are equal to angles. For instance, arctan(x) = $\alpha$ for some angle $\alpha$ . Then $\tan(\alpha)\, =\, x$ . Note that you have a numerical value for x.

Pick an angle variable for arctan(y), and plug the sum of these two angles, being the sum of the arctangents, into the angle-sum formula for tangent. Simplify the result, and plug in values where you can. I haven't completed the computations, but I believe that this process should lead you to the answer. :wink:

by **mathnoob** on Fri Aug 07, 2009 12:56 am

It simplified to (x+y)/(1-xy) which worked out right.
Thanks!

The Purplemath Forums

if x=1/2 and (x+1)(y+1)=2, find rad. meas of arctanx+arctany

if x=1/2 and (x+1)(y+1)=2, find rad. meas of arctanx+arctany

Re: if x=1/2 and (x+1)(y+1)=2, find rad. meas of arctanx+arctany

Re: if x=1/2 and (x+1)(y+1)=2, find rad. meas of arctanx+arctany

Re: if x=1/2 and (x+1)(y+1)=2, find rad. meas of arctanx+arctany