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Tan A = a / (a + 1) tan B = 1 / (2 a + 1)

Cot A = 1 + 1/a Cot B = 2a +1

Tan (A+B) = (Tan A + Tan B) / [1 - Tan A tan B]

= (Cot A + Cot B) / [Cot A Cot B - 1]

= (1 + 1/a + 2a +1) / [1 + 2a + 2 + 1/a - 1]

= [2 a² + 2 a + 1] / [2a² + 2a + 1]

= 1

=> A + B = π/4 or 5 π/4 : nπ + π/4

Cot A = 1 + 1/a Cot B = 2a +1

Tan (A+B) = (Tan A + Tan B) / [1 - Tan A tan B]

= (Cot A + Cot B) / [Cot A Cot B - 1]

= (1 + 1/a + 2a +1) / [1 + 2a + 2 + 1/a - 1]

= [2 a² + 2 a + 1] / [2a² + 2a + 1]

= 1

=> A + B = π/4 or 5 π/4 : nπ + π/4