Question

If sin(alpha - beta) = 1/2 and cos(alpha+beta) = 1/2, where alpha and beta are positive angles, then
a) alpha=45°, beta=15° b) alpha=15°, beta=45° c) alpha=60°, beta=15° d)NOTA

Answer 1

Answer:

The correct option is (a)

Step-by-step explanation:

$\alpha - \beta = \sin ^{ - 1} ( \frac{1}{2} ) = 30 \\ \alpha + \beta = \ \cos ^{ - 1} ( \frac{1}{2} ) = 60 \\ 2 \alpha = 90 \\ \alpha = 45 \\ \beta = 15$