Maths

Show that Cos 22.5=√2+√2/2

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asked by Ande2
  1. 22.5° = 45° / 2

    cos 45° = √ 2 / 2

    cos ( θ / 2 ) = ± √ [ ( 1 + cos θ ) / 2 ]

    45° is located in first quadrant where all trigonometric functions are positive so:

    cos 22.5° = cos ( 45° / 2 ) = √ [ ( 1 + cos 45° ) / 2 ] =

    √ [ ( 1 + √ 2 / 2 ) / 2 ] = √ [ ( 2 / 2 + √ 2 / 2 ) / 2 ] =

    √ [ ( 2 + √ 2 ) / 2 / 2 ] = √ [ ( 2 + √ 2 ) / 4 ] =

    √ ( 2 + √ 2 ) / √ 4 = √ ( 2 + √ 2 ) / 2

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    posted by Bosnian

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