AP EAMCET201822 Apr 2018Morning ShiftMathematicsInverse Trigonometric FunctionsActual
Let x, y be real numbers such that x y and x y 1 . If a x+b ( ⁻¹ x )=c and a y+b ( ⁻¹ y )=c , then x+y 1-x y =
Options
- A2 a b a^2-b^2
- B2 a c a^2+c^2
- C2 a b a^2+b^2
- D2 a c a^2-c^2 ⁻¹ 1
Correct answer
D. 2 a c a^2-c^2 ⁻¹ 1
Step-by-step solution
Let x= , then we have aligned & & a +b & =c & & a +b & =c & & c -a b & =b Let & & a^2+c^2 & =r^2 aligned Let So, for some , aligned & c=r , & a=r aligned Also, = a c Thus, - = b r ( + )= b r + = ⁻¹ b r Let + be the positive solution and + the negative solution, where aligned & y= & + =-( + ) & -2 = + & (-2 x)= ( + ) & -2 1- ^2 = ( + ) & -2 a / c 1-a^2 / c^2 = x+y 1-x y 2 a c a^2-c^2 = x+y 1-x y . aligned