Question

If tanA=a/a+1& tanB=1/2a+1, then find the value of (A+B)

Answer 1

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

Answer 2

Answer:

π÷4

Step-by-step explanation:

$tana = \frac{a}{a + 1} \\ tanb = \frac{1}{2a + 1} \\ cota = \frac{a + 1}{a} \\ cotb = 2a + 1 \\ tan(a + b) = \frac{tana + tanb}{1 - tanatanb} \\ = \frac{cota + cotb}{cotacotb - 1} \\ = ( \frac{a + 1}{a} + 2a + 1) \div ( \frac{a + 1}{a} \times (2a + 1) - 1) \\ = ((2 {a}^{2} + 2a + 1) \div a)\div((2 {a}^{2} + 2a + 1) \div a) \\ = 1 \\ \\ \\ tan(a + b) = 1 \\ therefore \: a + b = 45 degree$

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