The solution of the system of equations `sinxsiny=(sqrt(3))/4,cosxcosy=(sqrt(3))/4` are `x_1=pi/3+pi/2(2n+k); n , k in I` `y_1=pi/6+pi/2(k-2n); n , k in I` `x_2=pi/6+pi/2(2n+k); n , k in I` `y_2=pi/3+pi/2(k-2n); n , k in I`

Explanation

To solve the system of equations given by:

1. \( \sin x \sin y = \frac{\sqrt{3}}{4} \)
2. \( \cos x \cos y = \frac{\sqrt{3}}{4} \)

we will follow a systematic approach.

### Step 1: Rewrite the equations
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