Question

if tan(A +B) is equal to 1 and tan(A - B) is equal to 1 by root 3 find A and B ?​

Answer 1

tan(a+b)=1

$tan(a - b) = \frac{1}{ \sqrt{3} } \\ tan(a + b) = tan45 \\ a + b = 45..... \: \: \: 1\\ tan(a - b) = tan30 \\ a - b = 30 ...... \: \: \: \: \: 2\\ by \: solving \: eq \: 1 \: and \: 2 \: we \: get \: a = \frac{75}{2} \\ b = \frac{15}{2}$

hope it will help you

Answer 2

Answer:

tan(A+B)=1

⇒tan(A+B)=tan 45°

⇒A+B=45°

tan(A-B)=1/√3

⇒tan(A-B)=tan 30°

⇒A-B=30°

Now,

       A+B=45

      A-B=30

        2A=75

⇒A=75/2

Put value of A in A-B=45,

A+B=45

⇒75/2+B=45

⇒B=45/1-75/2

⇒B=15/2.

may it'll help you.