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

  • question_answer
    If \[\sin \theta +\cos \theta =m\]and \[\sec \theta +\text{cosec}\theta =n\], then \[n(m+1)(m-1)=\]       [MP PET 1986]

    A) m

    B) n

    C) 2m

    D) 2n

    Correct Answer: C

    Solution :

    \[n({{m}^{2}}-1)=(\sec \theta +\text{cosec}\theta ).2\sin \theta \cos \theta \]   (\[\because {{m}^{2}}=1+2\sin \theta \cos \theta \]) \[=\frac{\sin \theta +\cos \theta }{\sin \theta .\cos \theta }.2\sin \theta \cos \theta =2m\].


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