Work out what relationships you have, and how they can be converted to others. Then use those relationships and substitute them for other simpler ones. Often these will allow you to simplify a furtehr step. Keep going until it can't get any simpler.
Beyond that, it takes practise to notice the patterns and straight-up memory to know what turns into what.
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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.
Trigonometric identities involve certain functions of one or more angles. These identities are useful whenever expressions involving trigonometric functions need to be simplified.
Just as with any other identity, a trigonometric identity is a trigonometric statement (other than a definition), which is true for all values of the variable or variables.
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They can be used to simplify expressions so that the solutions can be found more easily.