Power Reduction
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 38 of 52.
Solve cos(2x) = 2cos(x)² - 1 for the square and you get a way to remove a power:
cos(x)² = (1 + cos(2x))/2
sin(x)² = (1 - cos(2x))/2
A square becomes a first power of a double angle, which is easier to integrate and, as the next lesson shows, to graph.
Take 2cos(x)². Replace the square: 2(1 + cos(2x))/2. Split the fraction into 1/2 + cos(2x)/2, Expand the 2 in front, and the line reads 1 + cos(2x).
Challenge
Show that 2sin(x)² equals 1 - cos(2x): rewrite it until the board reads 1 - cos(2x). Then press Check.
Try it yourself
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 Angles2Reciprocal 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