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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If \[se{{c}^{2}}\theta +ta{{n}^{2}}\theta =\sqrt{2}\], then the value of \[\left( \mathbf{se}{{\mathbf{c}}^{\mathbf{4}}}\theta -\mathbf{ta}{{\mathbf{n}}^{\mathbf{4}}}\theta  \right)\] is

    A) \[\frac{1}{\sqrt{3}}\]

    B) 1

    C) \[\sqrt{2}\]

    D) 0

    Correct Answer: C

    Solution :

    (c):- \[se{{c}^{2}}\theta +ta{{n}^{2}}\theta =\sqrt{2}\] and \[se{{c}^{2}}\theta -ta{{n}^{2}}\theta =1\] \[\therefore se{{c}^{4}}\theta -ta{{n}^{4}}\theta \] \[=\left( se{{c}^{2}}\theta +ta{{n}^{2}}\theta  \right)\left( se{{c}^{2}}\theta -ta{{n}^{2}}\theta  \right)\] \[=\sqrt{2}\times 1=\sqrt{2}\]


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