AP EAMCET201823 Apr 2018Morning ShiftMathematicsInverse Trigonometric FunctionsActual
If ⁻¹ ( x 2 )+ ⁻¹ ( y 2 )= , then 9 x^2-12 x y +4 y^2=
Options
- A36 ^2
- B37 ^2
- C39 ^2
- D36 ^2
Correct answer
A. 36 ^2
Step-by-step solution
We have, aligned & ⁻¹ ( x 2 )+ ⁻¹ ( y 3 )= & ⁻¹ [ x 2 y 3 - (1- ( x 2 )^2 ) (1- ( y 3 )^2 ) ]= & x 2 y 3 - (1- ( x 2 )^2 ) (1- ( y 3 )^2 ) = & = x y 6 - = (1- ( x 2 )^2 ) (1- ( y 3 )^2 ) aligned squaring both sides, we get aligned & ( x y 6 - )^2= (1- x^2 4 ) (1- y^2 9 ) & aligned x^2 y^2-12 x y +36 ^2 x 36 = (4-x^2 ) (9-y^2 ) 36 & =36-9 x^2-4 y^2+x^2 y^2 x^2 y^2-12 x y +36 ^2 x & =36 (1- ^2 ) aligned & 9 x^2-12 x y +4 y^2=36 ^2 aligned