Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX D - Trigonometry - D Exercises: 56

Answer

$tanx+tany=\frac{sin(x+y)}{cosxcosy}$

Work Step by Step

We need to prove the identity $tanx+tany=\frac{sin(x+y)}{cosxcosy}$ Let us solve the right side of the given identity. $\frac{sin(x+y)}{cosxcosy}=\frac{sinxcosy+cosxsiny}{cosxcosy}$ $\frac{sin(x+y)}{cosxcosy}=\frac{sinx}{cosx}+\frac{siny}{cosy}$ Hence, $tanx+tany=\frac{sin(x+y)}{cosxcosy}$
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