For parametric equations x = a(cos t + t sin t) and y = a(sin t − t cos t), what is d²y/dx²? A. sec²t / (at) B. sec³t / (at) C. tan t D. sec³t / a Answer: B) sec³t / (at) Explanation: dx/dt = at cos t, dy/dt = at sin t. dy/dx = tan t. d²y/dx² = d/dt(tan t) × (dt/dx) = sec²t × (1 / at cos t) = sec³t / (at).

imo class 12 continuity and differentiability

For parametric equations x = a(cos t + t sin t) and y = a(sin t − t cos t), what is d²y/dx²?

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For parametric equations x = a(cos t + t sin t) and y = a(sin t − t cos t), what is d²y/dx²?

Answer: B) sec³t / (at)

Explanation: dx/dt = at cos t, dy/dt = at sin t. dy/dx = tan t. d²y/dx² = d/dt(tan t) × (dt/dx) = sec²t × (1 / at cos t) = sec³t / (at).