Let A and B be acute angles measured counterclockwise from the positive x -axis. If the point P(2x+1, 1) lies on the terminal side of angle A and the point Q(x+1, x) lies on the terminal side of angle B , where x > 0 , then the value of A + B is:

Step-by-step solution

From the given coordinates, the tangent of the angles can be found using = y x . For angle A , the point is P(2x+1, 1) , so: A = 1 2x+1 For angle B , the point is Q(x+1, x) , so: B = x x+1 Using the tangent addition formula: (A+B) = A + B 1 - A B Substitute the values of A and B : (A+B) = 1 2x+1 + x x+1 1 - ( 1 2x+1 ) ( x x+1 ) (A+B) = (x+1) + x(2x+1) (2x+1)(x+1) (2x+1)(x+1) - x (2x+1)(x+1) (A+B) = x + 1 + 2x^2 + x 2x^2 + 3x + 1 - x (A+B) = 2x^2 + 2x + 1 2x^2 + 2x + 1 = 1 Since x > 0 , we have 0 Therefore, 0 Since