# Thread: Sum of a Tangent

1. ## Sum of a Tangent

If tan(x+y) = 33 and tan x = 3, find tan y.

I plugged these values into the Sum of a Tangent Identity:

$\displaystyle \tan \left( {\theta _1 + \theta _2 } \right) = \frac{{\tan \theta _1 + \tan \theta _2 }}{{1 - \tan \theta _1 \tan \theta _2 }}$

$\displaystyle \tan \left( {3 + y } \right) = \frac{{3 + \tan y }}{{1 - 3 \tan y }}$

$\displaystyle 33 = \frac{{3 + \tan y }}{{1 - 3 \tan y }}$

I solved for tan y and got: $\displaystyle \tan y = 3/10$

Is this the correct way to solve/correct answer? Thanks.

2. Originally Posted by lightningstab714
If tan(x+y) = 33 and tan = 3, find tan y.

I plugged these values into the Sum of a Tangent Identity:

$\displaystyle \tan \left( {\theta _1 + \theta _2 } \right) = \frac{{\tan \theta _1 + \tan \theta _2 }}{{1 - \tan \theta _1 \tan \theta _2 }}$

$\displaystyle \tan \left( {3 + y } \right) = \frac{{3 + \tan y }}{{1 - 3 \tan y }}$

$\displaystyle 33 = \frac{{3 + \tan y }}{{1 - 3 \tan y }}$

I solved for tan y and got: $\displaystyle \tan y = 3/10$

Is this the correct way to solve/correct answer? Thanks.
correct