Question

if tan A = a/a+1 and tan B = 1 / 2a+1 ,then the value of A +B is A)0 B) π /2 c) π /3 D ) π /4​

Answer 1

π÷4

Step-by-step explanation:

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

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