Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises - Page 680: 98


$\frac{\sin(s+t)}{\cos s\cos t}=\tan s+\tan t$

Work Step by Step

Start with the left side: $\frac{\sin(s+t)}{\cos s\cos t}$ Expand using the addition formula for sine: $=\frac{\sin s\cos t+\cos s\sin t}{\cos s\cos t}$ Break it into two fractions and simplify: $=\frac{\sin s\cos t}{\cos s\cos t}+\frac{\cos s\sin t}{\cos s\cos t}$ $=\frac{\sin s}{\cos s}+\frac{\sin t}{\cos t}$ $=\tan s+\tan t$ Since this equals the right side, the identity has been proven.
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