Trigonometric EquationHard

Question

The distance, from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t − 2t cos t at t =π/4,is :

Options

A.4
B.√2
C.2
D.2√2

Solution

= - 2sin t + 2sin t + 2t cos t = 2t cost
= 2cos t - 2cos t + 2 t sin t = 2t sin t
So = tan t
slope of normal = -

equation of normal a + t =
y - √2 + = - 1 (x - √2 - )
x + y - 2 √2 = 0
distance of normal form
= = 2

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