ACT-Style: Trig Identity Simplification

ACT Math · Axiom Academy

Combining trig fractions and spotting the Pythagorean identity — the core ACT simplification move. Simplify the expression into a single trig expression, using the identities the ACT expects you to know. Nice work — you turned a sum of two trig fractions into one clean expression using a common denominator and the Pythagorean identity. Combine first: when you add or subtract trig fractions, get a common denominator before anything else. Watch the numerator: after combining, almost always appears — spot it and replace it. The ACT tests only about five identities — no double-angle, sum/difference, or half-angle. Master the Pythagorean, quotient, and reciprocal identities and you can simplify anything on the test.

This is the written version of the interactive lesson above. See the full ACT Math course.