AP EAMCET202420 May 2024Morning ShiftMathematicsInverse Trigonometric FunctionsActual
If ^4 8 + ^4 3 8 + ^4 5 8 + ^4 7 8 =k then ⁻¹ ( k 2 )+ ⁻¹ ( k 3 )=
Options
- A2 3
- B3 4
- C4
- D2
Correct answer
A. 2 3
Step-by-step solution
^4 8 + ^4 3 8 + ^4 5 8 + ^4 7 8 = ^4 8 + ^4 3 8 + ^4 ( 2 + 8 )+ ^4 ( 2 + 3 8 )= ^4 8 + ^4 3 8 + ^4 8 + ^4 3 8 = ( ^4 8 + ^4 8 )+ ( ^4 3 8 + ^4 3 8 ) aligned &= ( ^2 8 + ^2 8 )^2-2 ^2 8 ^2 8 &+ ( ^2 3 8 + ^2 3 8 )^2-2 ^2 3 8 ^2 3 8 aligned =2- 1 2 ^2 4 - 1 2 ^2 3 4 =2- 1 2 ( 1 2 )^2- 1 2 ( 1 2 )^2= 3 2 =k Now, ⁻¹ k 2 + ⁻¹ ( k 3 )= ⁻¹ 3 2 + ⁻¹ 1 2 = 3 + 3 = 2 3