Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.2 - Sum and Difference Formulas - 5.2 Problem Set - Page 289: 52

Answer

See the steps.

Work Step by Step

$\sin{(90+x)} = \sin{90} \cos{x} + \sin{x} \cos{90} $ $\sin{(90+x)} = 1 \times \cos{x} + \sin{x} \times 0 = \cos{x}$ $\sin{(90-x)} = \sin{90} \cos{x} - \sin{x} \cos{90} $ $\sin{(90-x)} = 1 \times \cos{x} - \sin{x} \times 0 = \cos{x}$ $LHS = \sin{(90+x)} -\sin{(90-x)} = \cos{x} - \cos{x} = 0 $ $\therefore LHS = RHS$
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