Question

If sin (A+B)=1 and tan (A-B)=1/sqroot 3

are acute angles. find out the value of A and B​

Answer 1

A = 60° , B = 30°

Explanation:

`sin(A+B ) = 1\\\\\ \ \ (A + B) \ = \ \ sin^(-1) 1\\\\A + B = 90^\circ --(1)\\\\ \ tan (A - B) = (1)/(√(3))\\\\(A-B) = tan^(-1)(1)/(\sqrt3)}\\\\A - B = 30^\circ --(2)\\\\ (1) + (2) => 2A = 120^\circ\\`

`A = 60^\circ`

`from \ (1) \\A + B = 90^\circ\\60^\circ + B = 90^\circ\\B = 90^\circ - 60^\circ\\B = 30^\circ`