Question

If A - B = 41°, find the degree measure of angle A when tanA + tanB + tanAtanB = 1. A and B are both acute angles.

Answer 1

Answer:

The value of angle A is 43°  and

The value of angle B is 2°   .

Step-by-step explanation:

Given as :

A - B = 41°                 .....1

And , tan A + tan B + tan A tan B = 1

Or,  tan A + tan B = 1 - tan A tan B           ....2

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

Or, tan ( A + B ) = $\frac{1 - tanAtanB}{1 - tanAtanB}$            (from eq 2)

∴  tan ( A + B ) = 1

   A + B =  $tan^{-1}1$

I.e A + B = 45°                        ........3

Now, from eq 1 and eq 3

A - B = 41°    

A + B = 45°  

Or, (  A - B  ) + (  A + B ) = 41° + 45°    

Or,  2 A = 86°

∴   A = $\frac{86}{2}$ = 43°

Now, putting the value of angle A in eq 1

I.e A - B = 41°            

Or, B =  43° -  41° = 2°

Hence The value of angle A is 43°  and The value of angle B is 2°   .  Answer