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

  • question_answer
    \[\tan 1{}^\circ \tan 2{}^\circ \tan 3{}^\circ \tan 4{}^\circ ........\tan 89{}^\circ =\]  [MP PET 1998, 2001; AMU 1999; Pb. CET 1994]

    A) 1

    B) 0

    C) \[\infty \]

    D) 1/2

    Correct Answer: A

    Solution :

      \[\tan 1{}^\circ \tan 2{}^\circ ....\tan 89{}^\circ \] \[=(\tan 1{}^\circ \tan 89{}^\circ )(\tan 2{}^\circ \tan 88{}^\circ )......\]\[=1\times 1\times 1....=1.\]


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