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  5. Introduction to Trigonometry

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

  • question_answer
    If \[\tan A+\cot A=4,\] then \[{{\tan }^{4}}A+{{\cot }^{4}}A=\]

    A) 196

    B) 194

    C) 192

    D) 190

    Correct Answer: B

    Solution :

    [b] \[{{(\tan A+\cot A)}^{2}}={{4}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,{{\tan }^{2}}A+{{\cot }^{2}}A+2=16\]
    \[\Rightarrow \,\,\,\,\,\,\,\,{{\tan }^{2}}A+{{\cot }^{2}}A=14\]
    \[\Rightarrow \,\,\,\,\,\,\,\,{{({{\tan }^{2}}A+{{\cot }^{2}}A)}^{2}}={{(14)}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,{{\tan }^{4}}A+{{\cot }^{4}}A+2=196\]
    \[\Rightarrow \,\,\,\,\,\,\,\,{{\tan }^{4}}A+{{\cot }^{4}}A=194\]


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