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

  • question_answer
    The value of \[\frac{{{\sin }^{4}}\theta -{{\cos }^{4}}\theta }{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }\]is:

    A) \[1\]

    B) \[-1\]

    C) \[0\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] \[\frac{{{\sin }^{4}}\theta -{{\cos }^{4}}\theta }{{{\sin }^{2}}\theta -{{\cos }^{2}}\theta }=\frac{({{\sin }^{2}}\theta -{{\cos }^{2}}\theta )({{\sin }^{2}}\theta +{{\cos }^{2}}\theta )}{({{\sin }^{2}}\theta -{{\cos }^{2}}\theta )}\]
    \[[{{a}^{2}}-{{b}^{2}}=(a-b)\,(a+b)]\]
    \[={{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1\]


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