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 227: 29



Work Step by Step

$$X=\frac{\tan100^\circ+\tan80^\circ}{1-\tan100^\circ\tan80^\circ}$$ From the identity of the sum of tangent: $$\frac{\tan A+\tan B}{1-\tan A\tan B}=\tan(A+B)$$ So here $X$ actually follows the above identity with $A=100^\circ$ and $B=80^\circ$. Therefore, $X$ can also be rewritten as $$X=\tan(100^\circ+80^\circ)$$ $$X=\tan180^\circ$$ $$X=0$$ which means $$\frac{\tan100^\circ+\tan80^\circ}{1-\tan100^\circ\tan80^\circ}=0$$
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