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SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (II)

  • question_answer
    If \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta =2,\]then the value of \[\cos \frac{\alpha +\beta }{2}\]is

    A) 1

    B) \[-1\]

    C) 0

    D) 0.5

    Correct Answer: C

    Solution :

    [c] \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta =2\] \[\Rightarrow \]   \[\sin \alpha =\sin \beta =1\]\[(\therefore sin\theta \le 1)\] \[\Rightarrow \]   \[\alpha =\beta =90{}^\circ \] \[\therefore \]      \[\cos \left( \frac{\alpha +\beta }{2} \right)=\cos 90{}^\circ =0\]


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