Find the equation of tangent to the curve given by ` x=2 sin^(3)t ,y=2 cos^(3)t` at a point where ` t=(pi)/(2)` ?

Explanation

To find the equation of the tangent to the curve defined by the parametric equations \( x = 2 \sin^3 t \) and \( y = 2 \cos^3 t \) at the point where \( t = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Find the coordinates of the point on the curve at \( t = \frac{\pi}{2} \).

1. **Calculate \( x \)**:
\[ x = 2 \sin^3\left(\frac{\pi}{2}\right) = 2 \cdot 1^3 = 2 \]
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