Two vectors of equal magnitude: |A + B| versus |A - B| and the angle between them

1. A.
   $\cos^{- 1}\left( \frac{- 7}{99} \right)$
2. B.
   $\cos^{- 1}\left( \frac{- 99}{101} \right)$
3. C.
   $\sin^{- 1}\left( \frac{- 99}{101} \right)$
4. D.
   $\sin^{- 1}\left( \frac{- 7}{99} \right)$

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1. A.
   $|\widehat{A} + \widehat{B}| = |\widehat{A} - \widehat{B}|\tan\frac{\theta}{2}$
2. B.
   $|\widehat{A} - \widehat{B}| = |\widehat{A} + \widehat{B}|\tan\frac{\theta}{2}$
3. C.
   $|\widehat{A} + \widehat{B}| = |\widehat{A} - \widehat{B}|\cos\frac{\theta}{2}$
4. D.
   $|\widehat{A} - \widehat{B}| = |\widehat{A} + \widehat{B}|\cos\frac{\theta}{2}$

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1. A.
   $\sin^{- 1}\left( \frac{3}{5} \right)$
2. B.
   $\sin^{- 1}\left( \frac{1}{3} \right)$
3. C.
   $\cos^{- 1}\left( \frac{3}{5} \right)$
4. D.
   $\cos^{- 1}\left( \frac{1}{3} \right)$

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1. A.
   $|\overrightarrow{A} - \overrightarrow{B}| = \sqrt{2}Rsin\left( \frac{\theta}{2} \right)$
2. B.
   $|\overrightarrow{A} + \overrightarrow{B}| = 2Rsin\left( \frac{\theta}{2} \right)$
3. C.
   $|\overrightarrow{A} + \overrightarrow{B}| = 2Rcos\left( \frac{\theta}{2} \right)$
4. D.
   $|\overrightarrow{A} - \overrightarrow{B}| = 2Rcos\left( \frac{\theta}{2} \right)$

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