Simplifying Trig Expressions Step by Step

Pre-Calculus · Axiom Academy

EXAMPLE Simplifying Trig Expressions Rewrite, combine over a common denominator, and apply a Pythagorean identity to reach simplest form. Simplify the expression to a single fraction, then write it in an equivalent product form. Nice work — you turned a difference of two terms into one clean fraction using a reciprocal identity, a common denominator, and the Pythagorean identity. Convert to sine and cosine first: rewriting exposes the structure. Common denominators combine terms: writing lets the two pieces merge. Spot the Pythagorean identity: is the key simplification. The same three moves — rewrite, combine, apply an identity — simplify most trig expressions you will meet.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.