If sin(A – B) = ½ ; cos(A + B) = ½ . Find the values of A and B.�

1.	If sin(A – B) = ½ ; cos(A + B) = ½ . Find the values of A and B.
Answer» ANSWER: GIVEN that $\sin(A - B) = \dfrac{1}{2} \\ \\ \cos(A + B) = \frac{1}{2}$ Now $\sin(A - B) = \dfrac{1}{2} \: \: \: \: \: \: \: . .........(1)\\ \\ and \: as \: we \: know \\ \\ sin30 \degree = \dfrac{1}{2} \: \: \: \: \: \: \: \: \: ..........(2) \\ \\ so \: using \: (1) \: and \: (2) \\ \\ A - B = 30 \degree \: \: \: \: \: \: ..........(<klux>3</klux>)$ And $\cos(A + B) = \dfrac{1}{2} \: \: \: \: \: \: \: .........(4)\\ \\$ $cos60 \degree = \dfrac{1}{2} \: \: \: \: \: \: ........(5)$ $using \: (4) \: and \: (5) \\ \\ A + B = 60 \degree \: \: \: \: \: \: \: .......(<klux>6</klux>)$ Adding (3) and (6) We get $2A = 90 \degree \\ \\ \boxed{ \boxed{ A = 45 \degree}}$ Putting VALUE of A in (6) $\boxed{ \boxed{ B = 15 \degree}}$

If sin(A – B) = ½ ; cos(A + B) = ½ . Find the values of A and B.

Answer»

$\sin(A - B) = \dfrac{1}{2} \\ \\ \cos(A + B) = \frac{1}{2}$

Now

$\sin(A - B) = \dfrac{1}{2} \: \: \: \: \: \: \: . .........(1)\\ \\ and \: as \: we \: know \\ \\ sin30 \degree = \dfrac{1}{2} \: \: \: \: \: \: \: \: \: ..........(2) \\ \\ so \: using \: (1) \: and \: (2) \\ \\ A - B = 30 \degree \: \: \: \: \: \: ..........(<klux>3</klux>)$