Question

if sin ( A-B ) = ½ , cos ( A+B ) = ½, then find A and B.​

Answer 1

Answer:

$\alpha = 45 \\ \\ \beta = 15$

Step-by-step explanation:

$\alpha - \beta = 30 \\ \\ \alpha + \beta = 60 \\ \\ 2 \alpha = 90 \\ \\ \alpha = 45 \\ \\ \beta = 60 - 45 = 15 \\ \\ \alpha = 45 \\ \\ \beta = 15$

Answer 2

EXPLANATION.

⇒ sin(A - B) = 1/2. - - - - - (1).

⇒ cos(A + B) = 1/2. - - - - - (2).

As we know that,

We can write equation as,

⇒ sin(A - B) = sin(30°). - - - - - (1).

⇒ cos(A + B) = cos(60°). - - - - - (2).

We get,

⇒ A - B = 30°. - - - - - (1).

⇒ A + B = 60°. - - - - - (2).

We get,

⇒ 2A = 90°.

⇒ A = 45°.

Put the value of A = 45° in equation (2), we get.

⇒ 45° + B = 60°.

⇒ B = 60° - 45°.

⇒ B = 15°.

Value of A = 45° & B = 15°.