Question

Prove that
tan-1 (1/7) + tan-1 (1/13) = tan-1(2/9)

Answer 1

let tanA = 1/7 and tanB = 1/13

then tan(A+B) = (tanA + tanB)/( 1 - tanAtanB)
= (1/7 + 1/13)/(1 - (1/7)(1/13) )
= (20/91) / (90/91) = 20/90 = 2/9

and if we let tanC = 2/9
then A + B = C

thus tan^-1 (1/7) + tan^-1 (1/13) = tan^-1 (2/9)

check with your calculator
take 2nd Tan (1/7) = 8.13010..
take 2nd Tan(1/13) = 4.39871
add them: 12.5288..
take 2nd Tan(2/9) = 12.5288..