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10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

  • question_answer
    The value of \[\frac{{{\tan }^{2}}60{}^\circ +4{{\cos }^{2}}45{}^\circ +3{{\sec }^{2}}30{}^\circ }{\text{cosec 30}{}^\circ +\sec \,60{}^\circ -{{\cot }^{2}}30{}^\circ }\] is

    A) \[9\]

    B) \[\frac{1}{9}\]

    C) \[3\]

    D) \[\frac{1}{3}\]

    Correct Answer: A

    Solution :

    [a] We have,  \[\frac{{{\tan }^{2}}60{}^\circ +4{{\cos }^{2}}45{}^\circ +3{{\sec }^{2}}30{}^\circ }{\cos ec\,30{}^\circ +\sec 60{}^\circ -{{\cot }^{2}}30{}^\circ }\]
    \[=\frac{{{(\sqrt{3})}^{2}}+4{{\left( \frac{1}{\sqrt{2}} \right)}^{2}}+3{{\left( \frac{2}{\sqrt{3}} \right)}^{2}}}{2+2-{{(\sqrt{3})}^{2}}}\]
    \[=\frac{3+2+4}{4-3}=9\]


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