Question

If tanA=1/2 & tanB=1/3 find A+B

Answer 1

tan(a+b)=tanA+tanB/1-tana.tanb
1/2+1/3
/1-1/2×1×3
5/6/5/6=1

Answer 2

If tan A = 1/2 and tan B = 1/3 then $(A + B) = 45^{\circ}$

Solution:

Given that

$tan A = \frac{1}{2}$

$tan B = \frac{1}{3}$

To find: A + B

$tan(A+B) = \frac{tanA+tanB}{1-TanAtanB}$

Substituting the given values we get,

$tan(A+B) = \frac{tanA+tanB}{1-TanAtanB}$

$tan(A+B ) = \frac{ \frac{1}{2} + \frac{1}{3}}{1- \frac{1}{2} \times \frac{1}{3}}$

On simplifying the above expression,

$tan(A+B ) = \frac{ \frac{5}{6}}{1- \frac{1}{6}}$

$tan(A+B ) = \frac{ \frac{5}{6}}{\frac{5}{6}}$

$tan(A+B ) = \frac{5}{6} \times \frac{6}{5} = 1$

$tan(A+B) = 1$

$\text{ we know that } tan 45^{\circ}=1$

Therefore,

$tan(A+B) =tan 45^{\circ}\\\\(A + B) = 45^{\circ}$

Thus $(A + B) = 45^{\circ}$

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