# Find the value of A and B if A>0 and B

$\text{Using Prosthaphaeresis Formula,} \cos\alpha+\cos\beta=2\cos\dfrac{\alpha+\beta}2\cos\dfrac{\alpha-\beta}2\\ \text{and using Double angle formula, } \cos(\alpha+\beta)=2\cos^2\dfrac{\alpha+\beta}2-1 \\ \text{ form a Quadratic equation in} \cos\dfrac{\alpha+\beta}2 \\ \text{As }\alpha,\beta \text{ are real, the discriminant must be non-negative, but } \\\cos\dfrac{\alpha+\beta}2\le1$