You start wit one side of the identity and, using logical steps, show that it is equivalent to the other side. Or, you start with both sides and show that they both equivalent to some common expression.
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In trigonometry, identities are mathematical expressions that are true for all values of the variables involved. Some common trigonometric identities include the Pythagorean identities, the reciprocal identities, the quotient identities, and the double angle identities. These identities are used to simplify trigonometric expressions and solve trigonometric equations.
Unlike equations (or inequalities), identities are always true. It is, therefore, not possible to solve them to obtain values of the variable(s).
Neither trigonometry nor any other subject can be used to prove questions. It may be possible to answer questions but that is another matter,
sin^2 (feta) + cos^2 (feta) = 1 sin (feta) / cos (feta) = tan (feta)
plane trigonometry spherical trigonometry