Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 228: 61


$$\sin2x=2\sin x\cos x$$ By writing $2x$ as the sum of $x$ and $x$ and apply the sine sum identity, the left side can be shown to be equal to the right side and therefore, the equation is an identity.

Work Step by Step

$$\sin2x=2\sin x\cos x$$ We start from the left side first. $$X=\sin2x$$ We write $2x$ as the sum of $x$ and $x$ then apply the sine sum identity, which states $$\sin(A+B)=\sin A\cos B+\cos A\sin B$$ $$X=\sin(x+x)$$ $$X=\sin x\cos x+\cos x\sin x$$ $$X=2\sin x\cos x$$ Therefore, 2 sides are shown to be equal. The equation thus is an identity.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.