Always or sometimes

Angles A, B and C are the angles of a triangle. Decide whether each of the following is an identity, always true for all triangles, or an equation, sometimes true. If you decide it is an equation find the solution or solutions and describe the corresponding triangle.

1. \sin(180^\circ - A) = \sin B
2. \cos A = -\cos(B+C)
3. \cos A = \sin(B+C)

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For younger learners see the similar question on NRICH involving only even and odd numbers.