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SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (II)

  • question_answer
    Value of \[\left( \begin{align}   & {{\sin }^{2}}7\frac{1{}^\circ }{2}+{{\sin }^{2}}82\frac{1{}^\circ }{2}+ \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}2{}^\circ \cdot ta{{n}^{2}}88 \\ \end{align} \right)\]is

    A) 1

    B) 2

    C) 0

    D) 4

    Correct Answer: B

    Solution :

    [b] \[{{\sin }^{2}}7\frac{1{}^\circ }{2}+{{\sin }^{2}}82\frac{1{}^\circ }{2}+{{\tan }^{2}}2{}^\circ {{\tan }^{2}}88{}^\circ \] \[={{\sin }^{2}}\left( 90{}^\circ -82\frac{1{}^\circ }{2} \right)+{{\sin }^{2}}82\frac{1{}^\circ }{2}+{{\tan }^{2}}(90{}^\circ -88{}^\circ )ta{{n}^{2}}88{}^\circ \]\[={{\cos }^{2}}82\frac{1{}^\circ }{2}+{{\sin }^{2}}82\frac{1{}^\circ }{2}+{{\tan }^{2}}88{{\cot }^{2}}88=1+1=2\]


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