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  5. Introduction to Trigonometry

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

  • question_answer
    \[({{\sec }^{4}}A-{{\sec }^{2}}A)=\]

    A) \[{{\tan }^{4}}A-{{\tan }^{2}}A\]

    B) \[{{\tan }^{2}}A+{{\tan }^{4}}A\]

    C) \[{{\tan }^{2}}A-{{\tan }^{4}}A\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] We have, \[({{\sec }^{4}}A-{{\sec }^{2}}A)\]
    \[={{\sec }^{2}}A({{\sec }^{2}}A-1)={{\sec }^{2}}A(1+{{\tan }^{2}}A-1)\]
    \[={{\sec }^{2}}A{{\tan }^{2}}A=(1+{{\tan }^{2}}A){{\tan }^{2}}A=({{\tan }^{2}}A+{{\tan }^{4}}A)\]


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