If tanA=1/3 and tanB=1/7 show that 2A+B=45`

Question

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Answer 1

if tan(a)=1/3, yuze invers tnagent tu get a=18.43494881 deg

& 2a=36.86989761 deg

tan(b)=1/7=0.14285714285714...

invers tan giv b=8.130102354 deg

2a+b=36.8698976+8.130102354=44.99999996 deg

Answer 2

tanA = 1/3, tanB = 1/7

Then tan(2A) = 2tanA/(1-tan^2A) = (2/3)/(1 - 1/9) = 3/4

tan(2A + B) = (tan2A + tanB)/(1 - tan2A.tanB)

tan(2A + b) = (3/4 + 1/7)/(1 - (3/4)(1/7))

tan(2A + B) = (21/28 + 4/28)/(1 - 3/28)

tan(2A + B) = (25/28)/(25/28) = 1

i.e. 2A + B = 45°