sin^2x + cos^2x = 1

Prerequisites

Pythagorean Theorem Show

Sin, Cos, and Tan Show

sin^2x + cos^2x = 1

Introduction

  • \sin^2x + \cos^2x = 1
    LaTeX formula:\sin^2x + \cos^2x = 1

Proof

  • Let's start with a right-angled triangle: a right angled triangle
  • And define some identities we already know: pythagorean theorem re-arranged sin equation re-arranged cos equation
  • If we substitute a and o into our first identity, we get: (h\, \sin \theta)^2 + (h\, \cos \theta)^2 = h^2
  • Simplifying, we get: \sin^2x + \cos^2x = 1