Short Answer

find the exact value of the expression
cos 255 $°$ - cos 195 $°$

cos255 $°$ -cos195 $° = = 0.7071067812$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Rewriting the expression

$\cos (270 ° - x) = - \sin x \cos (180 ° + x) = - \cos x \cos 255 ° = \cos (270 ° - 15 °) = - \sin 15 ° \cos 195 ° = \cos (180 ° + 15 °) = - \cos 15 °$

Step 2. Calculations

Now our expression becomes

$= \cos 255 ° - \cos 195 = \cos 15 ° - \sin 15 ° N o w w e k n o w t h a t \cos 15 ° = \sin 75 ° S o, \cos 15 ° - \sin 15 ° = \sin 75 ° - \sin 15 ° \sin x - \sin y = 2 \sin (\frac{x - y}{2}) \cos (\frac{x + y}{2}) S o, \sin 75 ° - \sin 15 ° = 2 (\sin 30 ° \cos 45 °) = 2 \frac{1}{2} \frac{1}{\sqrt{2}} = 0.7071067812$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

find the exact value of the expression
cos 255 $°$ - cos 195 $°$

Step by Step Solution

Step 1. Rewriting the expression

Step 2. Calculations

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

find the exact value of the expression cos 255° - cos 195°

Step by Step Solution

Step 1. Rewriting the expression

Step 2. Calculations

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find the exact value of the expression
cos 255 $°$ - cos 195 $°$