Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 75


$(\sin x+\cos x)^2=1+\sin 2x$

Work Step by Step

Start from the left side: $(\sin x+\cos x)^2$ Expand: $=\sin^2 x + 2\sin x\cos x+\cos^2 x$ Rearrange: $=\sin^2 x +\cos^2 x+ 2\sin x\cos x$ Use the identities $\sin^2 x +\cos^2 x=1$ and $2\sin x\cos x=\sin 2x$: $=1+ \sin 2x$ Since this is equal to the right side, the identity is proven.
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