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# Trignometric Identity watch

1. Could someone please prove this identity:

cos X + 3 cos 2X = 2
2. (Original post by aiman)
Could someone please prove this identity:
cos X + 3 cos 2X = 2
cos(x) + 3cos(2x) = 2
=> cos(x) + 3(2cos2(x) - 1) = 2 *Using identity cos(2x) = 2cos2(x) - 1
=> cos(x) + 6cos2(x) - 3 = 2

Let u = cos(x), so

=> 6u2 + u - 5 = 0

solve for u, and then use arcsin(u) to get solutions for x.
3. Thank you
4. b2-4ac=1+20x6=121
x=-1+-11/12
x=-1 or 5/6

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Updated: February 27, 2006
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