Final: Tangents to sin 2x

Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 44 of 48.

Prove the identity in the prompt. Only tangents appear on the left, and a sine of a double angle on the right.

Challenge

Prove that $\frac{2\tan\left(x\right)}{1+{\tan\left(x\right)}^{2}}$ equals $\sin\left(2x\right)$ : rewrite it until the board reads $\sin\left(2x\right)$ . Then press Check.

Try it yourself

\frac{2\tan x}{1+\tan^{2} x}

Rewrite as $\sin 2x$

Test yourself

This 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 = 1 Squares Erase the Signs Recap: the Circle Identity

4Even, Odd and Cofunctions

Negative Angles Even and Odd in a Proof Even and Odd Graphs Cofunctions Recap: Signs of Angles

7Double-Angle Formulas

sin 2x = 2 sin x cos x Three Forms of cos 2x Exact Values, Doubled Square, Then Double The Graph of 2 sin x cos x Recap: Double Angles

10Final Challenges

Final: Two AnglesFinal: Tangents to sin 2xFinal: An Exact Product Final: A Wave in Disguise Final: Two Squares Final: Choose the Form

2Reciprocal and Quotient

Identity or Equation?Secant, Cosecant, Cotangent Recap: Reciprocals

5Proving Identities

Work on One Side Rewrite in sin and cos Factor First Make One Fraction Proofs That Go Wrong Recap: Prove It

8Half Angles, Power Reduction

Power Reduction sin²x Is a Wave Half-Angle Values tan of a Half Angle Recap: Half Angles

3Pythagorean Identities

1 + tan²x = sec²x A Difference of Squares Squaring a Sum Recap: Three Forms

6Sum and Difference

sin(A + B) and sin(A - B)cos(A + B) and cos(A - B)Turning by 90° and 180°Read the Formula Backwards tan(A + B) and tan(A - B)Recap: Sum Formulas

9Product to Sum

Products to Sums Sums to Products Sums Over Sums Recap: Sum to Product