Final: Two Squares
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 51 of 52.
Prove the identity in the prompt. Both squares expand, and most of what they produce cancels.
Challenge
Prove that (sin(x) + cos(x))² + (sin(x) - cos(x))² equals 2: rewrite it until the board reads 2. Then press Check.
Try it yourself
(sin(x) + cos(x))^2 + (sin(x) - cos(x))^2
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Identities
1Identities on the Circle
sin²x + cos²x = 1Squares Erase the SignsIdentity or Equation?Recap: the Circle Identity4Even, Odd and Cofunctions
Negative AnglesEven and Odd in a ProofEven and Odd GraphsCofunctionsRecap: Signs of Angles7Double-Angle Formulas
sin 2x = 2 sin x cos xThree Forms of cos 2xExact Values, DoubledSquare, Then DoubleThe Graph of 2 sin x cos xRecap: Double Angles10Final Challenges
Final: Two AnglesFinal: Tangents to sin 2xFinal: An Exact ProductFinal: A Wave in DisguiseFinal: Two SquaresFinal: Choose the Form2Reciprocal and Quotient
The Quotient IdentitySecant, Cosecant, CotangentDividing by a FractionWhere They BreakRecap: Reciprocals5Proving Identities
Work on One SideRewrite in sin and cosFactor FirstMake One FractionProofs That Go WrongRecap: Prove It8Half Angles, Power Reduction
Power Reductionsin²x Is a WaveHalf-Angle Valuestan of a Half AngleRecap: Half Angles