Verifying Identities Step by Step

Pre-Calculus · Axiom Academy

Prove a trig identity by transforming one side until it matches the other. Verify the identity . We'll work on the more complicated left side and transform it, step by step, until it becomes the right side. Nice work — you verified by reshaping the left side one move at a time. Convert to sine and cosine: rewriting and as and turns an unfamiliar sum into ordinary fractions. Common denominator: combining over produces the numerator . Pythagorean identity: collapses the numerator, leaving . Result: splitting that fraction gives , matching the right side. The same playbook — convert to sine/cosine, combine fractions, then apply a known identity — verifies most trig identities you'll meet.

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