Question

If tan theta =1/2 and tan phi =1/3 then find the value of theta + phi

Answer 1

Answer:

$\theta+\phi=\frac{\pi}{4}$

Step-by-step explanation:

Formula used:

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

Given:

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

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

consider,

$tan(\theta+\phi)$

$=\frac{tan\theta+tan\phi}{1-tan\theta\:tan\phi}$

$=\frac{\frac{1}{2}+\frac{1}{3}}{1-(\frac{1}{2})(\frac{1}{3})}$

$=\frac{\frac{3+2}{6}}{1-\frac{1}{6}}$

$=\frac{\frac{5}{6}}{\frac{6-1}{6}}$

$=\frac{\frac{5}{6}}{\frac{5}{6}}$

$tan(\theta+\phi)=1$

$\implies\:\theta+\phi=\frac{\pi}{4}$

Answer 2

Answer:

π/4

Step-by-step explanation: