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

  • question_answer
    If \[\tan \theta +\cot \theta =2,\] then \[{{\tan }^{2}}\theta +{{\cot }^{2}}\theta \] equals:

    A) 4

    B) 6

    C) 2

    D) 1

    Correct Answer: C

    Solution :

    [c] We have, \[\tan \theta +\cot \theta =2\]
    Squaring both sides, we get \[{{(\tan \theta +\cot \theta )}^{2}}=4\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta +2\tan \theta \cot \theta =4\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta +2(1)=4\]  \[[\tan \theta \cot \theta =1]\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta =4-2=2\]


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