2 2 1 1 1 = 1 sin 2x 2  x c 2 2 1 4 2 = Example 6 1 Find 10xdx 2 Solution the identity cos 2x = 2 cos2 x 1 – 1 1 Cos 20 x = 2 cos2 10x 1, then cos2 10x = – 2 2 1 1 2 2 Then 2 1 1 =  sin 20x  x c 2 40 Example 7 Find = cos 6x Solution Using the identity cos 2x = cos2 x sin2 x – Cos 6 x = cos2 3x sin2 3x – (cos 3x dx = sin Hence 3x) (cos 3x sin 3x) cos 6x 2 2 45 =
1 2 1 2 = 1 2 x 1 sin 2x 2 2  c Example 6 = 1 2 1 4 Find 2 10xdx Solution the identity cos 2x = 2 cos2 x – 1 Cos 20 x = 2 cos2 10x – 1, then cos2 10x = 1 2 1 2 Then 2 1 1 2 2 = 1 2 x  1 40 sin 20x  c Example 7 Find = cos 6x Solution Using the identity cos 2x = cos2 x – sin2 x Cos 6 x = cos2 3x – sin2 3x Hence cos 6x (cos 3x sin 3x) dx = (cos 2 3x sin 2 3x) 45 =
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