Question

if sin( A + B ) = cos (A - B) = root over 3/2 and A,B ( A> B) are acute angles, find the values of A and B​

Answer 1

Answer :- A= 30° and B= 15°

Answer 2

Given:

$\star \: \sin(A + B) = \frac{ \sqrt{3} }{2} \\ \\ \star \: \cos \: (A - B) = \frac{ \sqrt{3} }{2}$

To find :

• The value of A and B .

Solution :

$\implies \: \sin(A + B) = \frac{ \sqrt{3} }{2} \\ \\ \implies \: \sin \: (A + B) = \sin \: 60 \degree \: \\ \\ \implies \: A + B = 60 \degree - - - (1)$

Now ,

$\implies \cos(A - B) = \frac{ \sqrt{3} }{2} \\ \\ \implies \: \cos \: (A - B) = \cos \: 30 \degree \\ \\ \implies \: A - B = 30 \degree - - - (2)$

• Add both equation 1 and 2 we get ,

=> 2A = 90°

=> A = 90°/2

=> A = 45 °

• Now put the value of A in equation 1 , we get

=> A+B = 60 °

=> B = 60° - 45°

=> B = 15 °

Hence , the value of A is 45° and B is 15°.