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anonymous

  • 5 years ago

find all solutions of the given equation in the interval [0,2pi] cosx=cos3x

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  1. anonymous
    • 5 years ago
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    \[\pi\] would work

  2. anonymous
    • 5 years ago
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    i guess 0 would work as well. and maybe \[\frac{\pi}{2}\]

  3. anonymous
    • 5 years ago
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    maybe write 4cos^3(x) - 3cos(x) = cos(3x) (as this is an identity i think (correct me if i am wrong) Then obviously: cos(x) = 4cos^3(x) - 3cos(x) hence 0 = 4cos(x)(cos^2(x) - 1) so you can tell right away that all the places where cos(x) vanishes in that interval are solutions. Next solve cos^2(x) -1 = 0 for x to find the others

  4. anonymous
    • 5 years ago
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    @Callum, yes, that is the correct identity. This is how I would do the problem.

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