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Math Help - cosine problem

  1. #1
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    cosine problem

    Can someone explain to me how cos(theta/2) can be recongfigured into The square root of (1/2+ cos(theta)/2). Thanks.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jarny View Post
    Can someone explain to me how cos(theta/2) can be recongfigured into The square root of (1/2+ cos(theta)/2). Thanks.
    We can use the double angle formula to get it:

    \cos \theta = \cos \left(2 \cdot \frac {\theta}{2} \right)

    = \cos^2 \left( \frac {\theta}{2} \right) - \sin^2 \left( \frac {\theta}{2} \right)

    = \cos^2 \left( \frac {\theta}{2} \right) - \left[ 1 - \cos^2 \left( \frac {\theta}{2} \right) \right]

    = 2 \cos^2 \left( \frac {\theta}{2} \right) - 1

    So we have: \cos \theta = 2 \cos^2 \left( \frac {\theta}{2} \right) - 1

    solving for \cos \left( \frac {\theta}{2} \right) we obtain the desired result
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