Question

if tanA=1-tanB/1+tanB, value of (A+B)​

Answer 1

Answer:

A + B = 45°

Step-by-step explanation:

Given-----> tanA = ( 1 - tanB ) / ( 1 + tanB )

To find ------> Value of ( A + B )

Solution------> ATQ,

=> tanA = ( 1 - tanB ) / ( 1 + tanB )

=> tanA ( 1 + tanB ) = ( 1 - tanB )

=> tanA + tanA tanB = 1 - tanB

=> tanA + tanB = 1 - tanA tanB

=> tanA + tanB = ( 1 - tanA tanB ) × 1

=> ( tanA + tanB ) / ( 1 - tanA tanB ) = 1

We know that ,

tan ( α + β ) = ( tanα + tanβ ) / ( 1 - tanα tanβ ) , applying it here , we get,

=> tan ( A + B ) = 1

We know that , tan45° = 1 , applying it here , we get,

=> tan ( A + B ) = tan45°

=> A + B = 45°