For $$\alpha and \beta$$ both being acute angles, it is given that $$\sin(\alpha + \beta) = 1, \cos(\alpha - \beta) = \frac{1}{2}$$. The values of $$\alpha and \beta$$ are:
$$\sin(\alpha + \beta) = 1$$
$$(\alpha + \beta) =Â 90^\circ$$ -------i
$$\cos(\alpha - \beta) = \frac{1}{2}$$
$$(\alpha - \beta) = 60^\circ$$ -------ii
Adding i and ii we get,
$$2(\alpha) = 150$$
$$(\alpha) = 75^\circ$$ and $$(\beta) = 15^\circ$$
Create a FREE account and get:
