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Mathematics
Henry Joseph
13 June, 11:05
Show that cos2x=cosx
+5
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Ally Johnston
13 June, 15:04
0
cos (2x) = cos x
2 cos^2 x - 1 = cos x using the double angle formula
2 cos ^2 x - cos x - 1 = 0
factor
(2 cos x+1) (cos x - 1) = 0
using the zero product property
2 cos x+1 = 0 cos x - 1 = 0
2 cos x = - 1 cos x = 1
cos x = - 1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values (2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120 + 360n x=-120 + 360n x = 0 + 360n where n is an integer
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