If x = cos t(3 - 2cos^2t) and y = sin t (3 - 2sin^2t), then find the value dy/dx of at t = π/4. ​

Question

If x = cos t(3 - 2cos²t) and y = sin t (3 - 2sin²t), then find the value of \(\frac{dy}{dx}\) at t = \(\frac{\pi}{4}\).

Answer 1

Given,

x = cos t(3 - 2cos²t)

Differentiating both sides with respect to t, we get

Differentiating both sides with respect to t, we get

∴ \(\frac{dy}{dx}]_{t=\frac{\pi}{4}}\)

\(= cot\,\frac{\pi}{4}=1\)