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

Answer:

A = 60° , B = 30°

Step-by-step explanation:

$sin(A+B ) = 1\\\\\ \ \ (A + B) \ = \ \ sin^{-1} 1\\\\A + B = 90^\circ --(1)\\\\ \ tan (A - B) = \frac{1}{\sqrt{3}}\\\\(A-B) = tan^{-1}\frac{1}{\sqrt3}}\\\\A - B = 30^\circ --(2)\\\\ (1) + (2) => 2A = 120^\circ$

                   $A = 60^\circ$

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