Factor First
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 22 of 52.
When every term shares a trig factor, take it out: the bracket left behind is often an identity. Prove sin(x)³ + sin(x)cos(x)² = sin(x). Both terms hold a sin x, so Take out the common trig factor: sin(x)(sin(x)² + cos(x)²). The bracket is 1, and sin x times 1 is sin x.
Factoring keeps the value; dividing does not. Dividing the expression by sin x would change what it equals, and lose the angles where sin x is 0. Take the factor out and keep it on the line.
Challenge
Prove that cos(x)²sec(x)² - tan(x)²cos(x)² equals cos(x)²: rewrite it until the board reads cos(x)². 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