AP EAMCET201825 Apr 2018Morning ShiftMathematicsDifferentiationActual
If x = sec θ - cos θ , y = sec n θ - cos n θ then d y d x =
Options
- Ay 2 + 4 x 2 + 4
- Bn y 2 + 4 x 2 + 4
- Cx 2 + 4 y 2 + 4
- Dn x 2 + 4 y 2 + 4
Correct answer
B. n y 2 + 4 x 2 + 4
Step-by-step solution
Given: x = sec θ - cos θ y = sec n θ - cos n θ Then, we have d x d θ = sec θ tan θ + sin θ     . . . i d y d θ = n sec n - 1 θ sec θ tan θ - n cos n - 1 θ - sin θ ⇒ d y d θ = n sec n θ tan θ + n cos n - 1 θ sin θ Now, d y d x = d y d θ d x d θ = n sec n θ tan θ + n cos n - 1 θ sin θ sec θ tan θ + sin θ = n sec n θ cos θ + cos n - 1 θ sec θ co