Solution 4.3:4f

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Using the addition formula for cosine, we can express
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Using the addition formula for cosine, we can express <math>\cos (v-\pi/3)</math>
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<math>\cos \left( v-{\pi }/{3}\; \right)</math>
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in terms of <math>\cos v</math> and <math>\sin v</math>,
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in terms of
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<math>\text{cos }v</math>
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and
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<math>\text{sin }v</math>,
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{{Displayed math||<math>\cos\Bigl(v-\frac{\pi}{3}\Bigr) = \cos v\cdot \cos\frac{\pi }{3} + \sin v\cdot \sin\frac{\pi}{3}\,\textrm{.}</math>}}
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<math>\cos \left( v-\frac{\pi }{3} \right)=\cos v\centerdot \cos \frac{\pi }{3}+\sin v\centerdot \sin \frac{\pi }{3}</math>
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Since <math>\cos v = b</math> and <math>\sin v = \sqrt{1-b^2}</math> we obtain
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{{Displayed math||<math>\cos\Bigl(v-\frac{\pi}{3}\Bigr) = b\cdot\frac{1}{2} + \sqrt{1-b^2}\cdot\frac{\sqrt{3}}{2}\,\textrm{.}</math>}}
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Since
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<math>\text{cos }v=b\text{ }</math>
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and
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<math>\sin v=\sqrt{1-b^{2}}</math>
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we obtain
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<math>\cos \left( v-\frac{\pi }{3} \right)=b\centerdot \frac{1}{2}+\sqrt{1-b^{2}}\centerdot \frac{\sqrt{3}}{2}</math>
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Current revision

Using the addition formula for cosine, we can express \displaystyle \cos (v-\pi/3) in terms of \displaystyle \cos v and \displaystyle \sin v,

\displaystyle \cos\Bigl(v-\frac{\pi}{3}\Bigr) = \cos v\cdot \cos\frac{\pi }{3} + \sin v\cdot \sin\frac{\pi}{3}\,\textrm{.}

Since \displaystyle \cos v = b and \displaystyle \sin v = \sqrt{1-b^2} we obtain

\displaystyle \cos\Bigl(v-\frac{\pi}{3}\Bigr) = b\cdot\frac{1}{2} + \sqrt{1-b^2}\cdot\frac{\sqrt{3}}{2}\,\textrm{.}
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