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, \[A=(x+y),\,\,B=(x-y)\] \[R=\sqrt{({{x}^{2}}+{{y}^{2}})}\] We get \[\theta \,\,=\,{{\cos }^{-1}}\,\left( -\frac{({{x}^{2}}+{{y}^{2}})}{2({{x}^{2}}-{{y}^{2}})} \right)\]You need to login to perform this action.
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