Strategy for Proving

Trigonometry · Axiom Academy

LESSON Strategies for Proving Trig Identities Master systematic approaches to prove even the most complex trigonometric identities with confidence When proving a trigonometric identity, you have three main strategies at your disposal. Each has its place, and often you'll combine them in a single proof. 1. Strategy: Work with the More Complex Side When to use: Almost always! Start by identifying which side of the identity has more terms, more different trig functions, or looks more complicated. Work with that side to simplify it into the simpler side. Example: To prove the identity shown above, we start with the left side because it has more terms and operations. The right side is simpler (1 + 2 sin θ cos θ), so we work to simplify the left side until it matches. 2. Strategy: Convert to Sines and Cosines When to use: When you have a mix of different trig functions (tangent, secant, cotangent, cosecant), convert them all to sines and cosines. This creates a common "language" that's easier to work with. Example: The animation shows how converting tan θ and sec θ into sines and cosines reveals a common factor that we can cancel, dramatically simplifying the expression. 3. Strategy: Apply Algebraic Techniques When to use: Once you've simplified using trig identities and conversions, treat the expression like an algebra problem. Factor, find common denominators, multiply by conjugates, or combine fractions.

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