Answer
See the steps.
Work Step by Step
$\sin{4x} + \sin{6x} = 2 \sin{5x} \cos{-x} = 2 \sin{5x} \cos{x}$
$\cos{4x} - \cos{6x} = -2 \sin{5x} \sin{-x} = 2 \sin{5x} \sin{x}$
$RHS = \dfrac{2 \sin{5x} \cos{x}}{2 \sin{5x} \sin{x}} = \cot{x}= LHS$
Trigonometry 7th Edition
by McKeague, Charles P.; Turner, Mark D.
Published by
Cengage Learning
ISBN 10:
1111826854
ISBN 13:
978-1-11182-685-7
Chapter 5 - Section 5.5 - Additional Identities - 5.5 Problem Set - Page 312: 46
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