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

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### 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 the radian measure of arctan (x) + arctan (y)

could someone help me get started please?
mathnoob

Posts: 8
Joined: Tue Jul 28, 2009 12:39 pm

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

Perhaps you should start by determining the value of y.
Honeysuckle588

Posts: 23
Joined: Wed Jul 15, 2009 4:07 pm

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

y = 1/3, but then what?
mathnoob

Posts: 8
Joined: Tue Jul 28, 2009 12:39 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.

stapel_eliz

Posts: 1729
Joined: Mon Dec 08, 2008 4:22 pm

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

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

Posts: 8
Joined: Tue Jul 28, 2009 12:39 pm