It means that you prove that an equation is true for ALL values of the variable or variables involved.
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Yes. Trigonometric identities are extremely important when solving calculus equations, especially while integrating.
Always. In fact, one method of proving a quadrilateral a rhombus is by first proving it a parallelogram, and then proving two consecutive sides congruent, diagonals bisecting verticies, etc.
identical identities
They are identities because they are true for ALL values of w and x.
Identities are statements that are true for any number.