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

  • question_answer
    \[({{\cos }^{4}}A-{{\sin }^{4}}A)\] is equal to:

    A) \[1-2{{\cos }^{2}}A\]

    B) \[2{{\sin }^{2}}A-1\]

    C) \[{{\sin }^{2}}A-{{\cos }^{2}}A\]

    D) \[2{{\cos }^{2}}A-1\]

    Correct Answer: D

    Solution :

    [d]\[({{\cos }^{4}}A-{{\sin }^{4}}A)={{({{\cos }^{2}}A)}^{2}}-{{({{\sin }^{2}}A)}^{2}}\]
    \[=({{\cos }^{2}}A-{{\sin }^{2}}A)({{\cos }^{2}}A+{{\sin }^{2}}A)\]
    \[=({{\cos }^{2}}A-{{\sin }^{2}}A)\,\,(1)\]
    \[={{\cos }^{2}}A-(1-{{\cos }^{2}}A)\]
    \[=2{{\cos }^{2}}A-1\]


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