In triangle ABC prove that
(i) `sinA=sin(B+C)" "(ii) sin2A=-sin(2B+2C)`
(iii)` cosA=-cos(A+B)" " (iv) tan((A+B)/2)=cot. C/2`

Explanation

To prove the statements in triangle ABC, we will use the properties of angles in a triangle and trigonometric identities.

### Given:
In triangle ABC, we know that the sum of angles is:
\[ A + B + C = 180^\circ \]
or in radians,
\[ A + B + C = \pi \]

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