CalcNotes0103-page13

# CalcNotes0103-page13 - To obtain Version 2 which contains...

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(Chapter 1: Review) 1.47 GROUP 3b: DOUBLE-ANGLE IDENTITIES FOR cos Memorize These Three Versions of the Double-Angle Identity for cos 2 u () : Let’s begin with the version we’ve already seen: Version 1: cos 2 u () = cos 2 u ± sin 2 u Also know these two, from “left-to-right,” and from “right-to-left”: Version 2: cos 2 u () = 1 ± 2sin 2 u Version 3: cos 2 u () = 2cos 2 u ± 1 Obtaining Versions 2 and 3 from Version 1 It’s tricky to remember Versions 2 and 3, but you can obtain them from Version 1 by using the Pythagorean Identity sin 2 u + cos 2 u
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Unformatted text preview: To obtain Version 2, which contains sin 2 u , we replace cos 2 u with 1 ± sin 2 u ( ) . cos 2 u ( ) = cos 2 u ± sin 2 u (Version 1) = 1 ± sin 2 u ( ) from Pythagorean Identity ± ² ³ ´ ³ ± sin 2 u = 1 ± sin 2 u ± sin 2 u = 1 ± 2 sin 2 u ( ² Version 2) To obtain Version 3, which contains cos 2 u , we replace sin 2 u with 1 ± cos 2 u ( ) . cos 2 u ( ) = cos 2 u ± sin 2 u (Version 1) = cos 2 u ± 1 ± cos 2 u ( ) from Pythagorean Identity ± ² ³ ´ ³ = cos 2 u ± 1 + cos 2 u = 2 cos 2 u ± 1 ( ² Version 3)...
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