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Burke
Mathematics
31 March, 12:28
Solve cos2x=cos^2x-1/2
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Jazlynn Cohen
31 March, 12:44
0
Hello:
by identity : cos (x+x) = cosx cosx-sinxsinx = cos² (x) - sin² (x)
but : cos² (x) + sin² (x) = 1
sin² (x) = 1-cos² (x)
cos (2x) = cos² (x) - (1-cos² (x))
cos (2x) = 2cos² (x) - 1
Solve cos (2x) = cos² (x) - 1/2
2cos² (x) - 1 = cos² (x) - 1/2
cos² (x) = 1/2
cos (x) = 1/√2 or cos (x) = - 1/√2
1) cos (x) = 1/√2 : in R x = π/4 + 2kπ or x = - π/4 + 2kπ
2) cos (x) = - 1/√2 in R x=5π/4 + 2kπ or x = - 5π/4 + 2kπ k in Z
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