Make One Fraction
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 23 of 52.
A sum with a fraction in it becomes one fraction over that fraction's bottom. The top then often holds a Pythagorean identity. Prove sin(x) + cos(x)²/sin(x) = csc(x). Write as one fraction over sin x: (sin(x)² + cos(x)²)/sin(x). The top is 1, so the fraction is 1/sin(x), which is csc x.
To put sin x over sin x, multiply it by sin x on top and below: that is why the first term lands on top as sin²x. Writing sin x on top unsquared changes the value.
Challenge
Prove that sec(x) - sin(x)tan(x) equals cos(x): rewrite it until the board reads cos(x). 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