Answer
See below.
Work Step by Step
$LHS=\frac{1}{tan(\alpha+\beta)}=\frac{1-tan(\alpha)tan(\beta)}{tan(\alpha)+tan(\beta)}\times\frac{cot(\alpha)cot(\beta)}{cot(\alpha)cot(\beta)}=\frac{cot(\alpha)cot(\beta)-1}{cot(\beta)+cot(\alpha)}=RHS$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 67
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