AP EAMCET202119 Aug 2021Morning ShiftMathematicsDifferentiationActual
If y = Tan - 1 1 + x 2 + 1 - x 2 1 + x 2 - 1 - x 2 , where x 2 ≤ 1 . Then find d y d x
Options
- Aπ 4 + 1 2 Cos − 1 ⁡ x 2
- Bπ 4 − 1 2 Cos − 1 ⁡ x 2
- C− x 1 − x 4
- D− 2 x 1 − x 4
Correct answer
C. − x 1 − x 4
Step-by-step solution
Given that y = Tan - 1 1 + x 2 + 1 - x 2 1 + x 2 - 1 - x 2 Put x 2   =   cos   2 θ ⇒ θ = 1 2 cos - 1 x 2   - - ( I ) y   =   tan - 1 1 + cos 2 θ + 1 - cos 2 θ 1 + cos 2 θ - 1 - cos 2 θ We know that cos   2 θ   =   1   -   2 sin 2 θ =   2 cos 2 θ   -   1 y   =   tan - 1 2 cos   θ   +   sin   θ 2 cos   θ   -   sin   θ y   =