Proofs That Go Wrong
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 24 of 52.
Four moves look like algebra and are not:
Cancelling a term of a sum. In (sin(x) + cos(x))/sin(x) the sin x cannot be crossed out: it is a term on top, not a factor. Split the fraction instead: 1 + cos(x)/sin(x).
Splitting a function. sin(2x) is not 2sin(x), and sin(x + y) is not sin(x) + sin(y): a function is not a number to multiply out.
Reading the square as the angle. sin(x)² squares the value, sin(x²) squares the angle.
Dividing by something that can be 0. Dividing by sin x is not allowed where sin x is 0; factor instead.
Challenge
Prove that (1 - sin(x)²)tan(x)² equals sin(x)²: rewrite it until the board reads sin(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