A vertical pole subtends an angle ⁻¹ ( 1 2 ) at a point P on the ground. If the angles substended by the upper half and the lower half of the pole at P are respectively and , then ( , ) is equal to

Step-by-step solution

Let A C be a pole and point P be the position on of the ground. Given, = ⁻¹ 1 2 = 1 2 Also, = + aligned & & = ( + ) & 1 2 & = + 1- aligned (a) When ( , )= ( 1 4 , 1 5 ) RHS = 1 4 + 1 5 1- 1 4 1 5 = 9 20 19 20 = 9 19 1 2 , not true (b) aligned & When ( , )= ( 1 5 , 2 9 ) & aligned RHS & = 1 5 + 2 9 1- 1 5 2 9 = 19 45 43 45 = & 19 43 1 2 , not true aligned aligned (c) When ( , )= ( 2 9 , 1 4 ) RHS = 2 9 + 1 4 1- 2 9 1 4 = 17 36 34 36 = 1 2 , true