10-2

tan theta=1/4
tan theta=3/5
tan(theta+beta)=tan(1/4+3/5)=tan theta+tan beta/1-tan theta*tan beta
(1/4)+(3/5)/1-(1/4)*(3/5)=5/20+12/20/1-3/20=17/20/17/20=1

In this problem, you are given tan theta and tan beta.  First to solve this problem, you need to know the formula.  The formula that you need is tan theta+tan beta/1-tan theta*tan beta.  Now that you have the formula, you just plug in the numbers you are given into the formula.  So now you have 1/4+3/5/1-1/4*3/5.  First in solving this equation, you have to find common denominators so you can add the top two fractions.  20 is the common denominator I used, so I had 5/20+12/20.  That gave me 17/20.  Next for the bottom half of the equation, you multiply the two fractions first and get 1-3/20.  Then you subtract 1 form 3/20 and get 17/20.  Now you have 17/20/17/20.  That equals 1.