A) \[{{\cos }^{-1}}\left[ -\frac{{{x}^{2}}+{{y}^{2}}}{2({{x}^{2}}-{{y}^{2}})} \right]\]
B) \[{{\cos }^{-1}}\left[ \frac{-2({{x}^{2}}-{{y}^{2}})}{{{x}^{2}}+{{y}^{2}}} \right]\]
C) \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}+{{y}^{2}})}{({{x}^{2}}-{{y}^{2}})} \right]\]
D) \[{{\cos }^{-1}}\left[ -\frac{({{x}^{2}}-{{y}^{2}})}{({{x}^{2}}+{{y}^{2}})} \right]\]
Correct Answer: A
Solution :
\[{{R}^{2}}={{A}^{2}}+{{B}^{2}}+2AB\cos \theta \] Substituting,\[A=(x+y),\,\,B=(x-y)\]and \[R=\sqrt{({{x}^{2}}-{{y}^{2}})}\] we get,\[\theta ={{\cos }^{-1}}\left[ -\frac{({{x}^{2}}+{{y}^{2}})}{2({{x}^{2}}-{{y}^{2}})} \right]\]
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