Simplifying trigonometric expressions

If you get stuck trying to establish a trigonometric identity or solve a trigonometric equation, one strategy is to systematically simplify both sides (or to subtract them and simplify the result). By ‘simplify’ we really mean to put into a standard form, which is usually simpler than what you started with but not always. (Compare the process of rationalizing a denominator or expanding a factored polynomial.)

Here is a process for simplifying expressions with trigonometric operations:

If two sides of an identity are simplified in this manner, then they will be the same; similarly, an expression equivalent to 0 will simply to 0 in this way.

Instead of changing cos2 to sin2 and sinizing denominators, you can also change sin2 to cos2 and cosinize denominators. Just be consistent within a given problem.

This approach can also be extended to inverse trigonometric operations, but we don't need that for this class.

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This web page was written in 2014 by Toby Bartels, last edited on 2014 January 21. Toby reserves no legal rights to it.

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