Verifying cos(2θ) = 2cos²θ - 1

Algebra 2 · Axiom Academy

Derive the cosine double-angle identity from the angle addition formula and the Pythagorean identity. Verify the double-angle identity by starting from the angle addition formula for cosine and using the Pythagorean identity. Nice work — you derived the cosine double-angle identity from two building blocks you already knew. Here's what to remember: The angle addition formula is the foundation: becomes the double-angle formula when . The Pythagorean identity is the bridge: converts a mixed sine/cosine expression into a cosine-only one. Multiple equivalent forms exist: can also be written or — this derivation lands on just one of the three. The same substitute-and-simplify strategy verifies the sine and tangent double-angle formulas too.

This is the written version of the interactive lesson above. See the full Algebra 2 course.