If ( + ) = 3 5 and = 5 13 , where + lies in the IV ^ th quadrant and lies in the II ^ nd quadrant, then the value of and the quadrant in which lies, respectively are

Step-by-step solution

Given ( + ) = 3 5 and + is in the IV ^ th quadrant. So, ( + ) = - 4 5 and ( + ) = - 4 3 . Also given = 5 13 and is in the II ^ nd quadrant. So, = - 12 13 and = - 5 12 . We can write = ( + ) - . Using the formula (A - B) = A - B 1 + A B , we get: = ( + ) - 1 + ( + ) = - 4 3 - (- 5 12 ) 1 + (- 4 3 ) (- 5 12 ) = -16 + 5 12 1 + 20 36 = - 11 12 56 36 = - 11 12 36 56 = - 33 56 . To find the quadrant of , we check the signs of and : = (( + ) - ) = ( + ) - ( + ) = (- 4 5 ) (- 12 13 ) - ( 3 5 ) ( 5 13 ) = 48 65 - 15 65 = 33