Throughout, \(A\), \(B\) and \(C\) are the angles of a triangle.

For each of the following, decide whether it is an identity (true for all triangles) or an equation (there is a triangle for which it is not true).

If it is an identity, true for all triangles, then you should prove it (using trigonometric identities that you already know).

If it is an equation, then at the very least you should give an example of a triangle for which it is not true. You could also try to solve the equation (that is, find all triangles for which it is true).

To help you decide whether an expression is an equation or an identity, you could test it out on some particular triangles, perhaps using angles where you can easily evaluate the expression, or perhaps using particular types of triangle (isosceles or right-angled or equilateral, for example).

You might find it helpful to make a list of the trigonometric identities that you know, so that you can think about which, if any, might be helpful at any given moment.