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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If a line in the space makes angle\[\alpha \],\[\beta \]and\[\gamma \] with the coordinate axes, then\[\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta \]\[+{{\sin }^{2}}\gamma \] equals

    A) \[-1\]                                    

    B) \[0\]

    C) \[1\]                     

    D)        \[2\]

    Correct Answer: C

    Solution :

    \[\cos 2\alpha +\cos 2\beta +\cos 2\gamma +{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta \]                                                                 \[+{{\sin }^{2}}\gamma \] \[=({{\cos }^{2}}\alpha -{{\sin }^{2}}\alpha )+({{\cos }^{2}}\beta -{{\sin }^{2}}\beta )\] \[+({{\cos }^{2}}\gamma -{{\sin }^{2}}\gamma )+{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \] \[={{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma \] \[=1\]


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