JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

  • question_answer
    \[(\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A=\][Roorkee 1972]

    A) \[\sec A\]

    B) \[2\sec A\]

    C) 0

    D) 1

    Correct Answer: C

    Solution :

    \[(\sec A+\tan A-1)(\sec A-\tan A+1)-2\tan A\] \[=({{\sec }^{2}}A-{{\tan }^{2}}A)+\sec A+\tan A-\sec A\] \[+\tan A-1-2\tan A=0\]   \[(\because {{\sec }^{2}}A-{{\tan }^{2}}A=1)\]


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