Question

if tan(A+B)=(tanA+tanB)/(1-tanAtanB)
find tan20+tan25+tan25tan20

Answer 1

$tan(A+B)= \frac{tan A+tanB}{1-tanAtanB}\\ \\put\ A=20,\ B=25\\ \\ tan(20+25)= \frac{tan 20+tan25}{1-tan20tan25}\\ \\ tan(45)= \frac{tan 20+tan25}{1-tan20tan25}\\ \\1= \frac{tan 20+tan25}{1-tan20tan25}\\ \\ tan 20+tan25=1-tan20tan25\\ \\tan 20+tan25+tan20tan25=\boxed 1$