Question

If x = cos t sin 2t and y = sin t cos 2t, then at t = `pi/4`, the value of `dy/dx` is equal to ______ 

Options

• -2

• 2

• `1/2`

• `-1/2`

Answer 1

If x = cos t sin 2t and y = sin t cos 2t, then at t = `pi/4`, the value of `dy/dx` is equal to 2.

Explanation:

x = cos t sin 2t and y = sin t cos 2t

∴ `dx/dt` = 2cos t cos 2t - sin t sin 2t and

`dy/dt` = cos t cos 2t - 2sin t sin 2t

∴ `dy/dx = (dy/dt)/(dx/dt) = (cos t cos 2t - 2sin t sin 2t)/(2cos t cos 2t - sint sin 2t)`

∴ `(dy/dx)_{(t = pi/4)} = (0 - 2 xx 1/sqrt2)/(0 - 1/sqrt2) = 2`