Question

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

Answer 1

Answer:

Given that

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

Now

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

And

$\cos(A + B) = \dfrac{1}{2} \: \: \: \: \: \: \: .........(4)$

$cos60 \degree = \dfrac{1}{2} \: \: \: \: \: \: ........(5)$

$using \: (4) \: and \: (5) \\ \\ A + B = 60 \degree \: \: \: \: \: \: \: .......(6)$

Adding (3) and (6)

We get

$2A = 90 \degree \\ \\ \boxed{ \boxed{ A = 45 \degree}}$

Putting value of A in (6)

$\boxed{ \boxed{ B = 15 \degree}}$