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

  • question_answer
    If \[x=\sec \theta +\tan \theta ,\]then \[x+\frac{1}{x}=\] [MP PET 1986]

    A) 1

    B) \[2\sec \theta \]

    C) 2

    D) \[2\tan \theta \]

    Correct Answer: B

    Solution :

    Given that \[x=\sec \theta +\tan \theta \] \[\Rightarrow \,x+\frac{1}{x}=\sec \theta +\tan \theta +\frac{1}{\sec \theta +\tan \theta }\] \[=\sec \theta +\tan \theta +\sec \theta -\tan \theta =2\sec \theta \]


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