Question

Assignment
If tun (A+B) =1/7 and tan A=1/3, find Tan B​

Answer 1

`- ( 2)/(11)`

Explanation:

`\tan (A + B) = (\tan A + \tan B)/(1 - \tan A . \tan B) \\ \\ (1)/(7) = ( (1)/(3) +\tan B )/(1 - (1)/(3) . \tan B) \\ \\ (1)/(7) = ( (1 + 3\tan B)/(3) )/( (3 -\tan B )/(3) ) \\ \\ (1)/(7) = (1 + 3\tan B)/(3 - \tan B) \\ \\ 7(1 + 3\tan B )= 3 - \tan B \\ \\ 7 + 21\tan B = 3 - \tan B \\ \\ 21\tan B + \tan B = 3 - 7 \\ \\ 22\tan B = - 4 \\ \\ \tan B = ( - 4)/(22) \\ \\\huge \purple {\boxed {\tan B = - ( 2)/(11)}}`