COMEDK2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
If A= 4 5 and B= -12 13 where A and B lie in first and third quadrant respectively. Then (A+B)=
Options
- A-16 65
- B-56 65
- C16 65
- D56 65
Correct answer
A. -16 65
Step-by-step solution
Given A = 4 5 and A is in the first quadrant, A = 1 - ^2 A = 1 - ( 4 5 )^2 = 1 - 16 25 = 9 25 = 3 5 . Given B = -12 13 and B is in the third quadrant, B = - 1 - ^2 B = - 1 - ( -12 13 )^2 = - 1 - 144 169 = - 25 169 = - 5 13 . Using the identity (A + B) = A B - A B , we substitute the values: (A + B) = ( 3 5 ) ( -12 13 ) - ( 4 5 ) ( -5 13 ) (A + B) = -36 65 - ( -20 65 ) (A + B) = -36 + 20 65 = -16 65 . Answer: -16 65