If `A ,\ B ,\ C ,\ D` be the angles of a cyclic quadrilateral, taken in order, prove that: `cos(180^@-A)+cos(180^@+B)+cos(180^@+C)-sin(90^@+D)=0`

Explanation

To prove the equation \( \cos(180^\circ - A) + \cos(180^\circ + B) + \cos(180^\circ + C) - \sin(90^\circ + D) = 0 \) for angles \( A, B, C, D \) of a cyclic quadrilateral, we will follow these steps:

### Step 1: Use the properties of cyclic quadrilaterals
In a cyclic quadrilateral, the sum of opposite angles is \( 180^\circ \). Therefore, we have:
\[ A + C = 180^\circ \quad \text{and} \quad B + D = 180^\circ \]

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