Question

If tan (A + B) = √3, tan (A - B) = 1

√3

, 0°

< A + B < 90°

, A > B, find A and B. Also calculate tan A sin

(A + B) + cos A tan (A - B).​

Answer 1

Step-by-step explanation:

tan(A+B) = √3                                           tan(A-B) = 1/√3

tan(A-B) = tan 60°--- 1)                             tan(A-B) = tan 30°

     

                                    solving 1 and 2        

 

A + B = 60

A - B   = 30

___________

2A = 90

A = 45°

Put eq. 1) in eq. 2)

=) A+ B = 60

=) 45 + B = 60

=) B = 60 - 45

=) B = 15

so, A = 45 and B = 15

Hope this helps u ^_^