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

  • question_answer
    If \[\sin \theta +\text{cosec}\theta =\text{2}\], then \[{{\sin }^{2}}\theta +\text{cose}{{\text{c}}^{\text{2}}}\theta =\] [MP PET 1992; MNR 1990; UPSEAT 2002]

    A) 1

    B) 4

    C) 2

    D) None of these

    Correct Answer: C

    Solution :

    \[{{\sin }^{2}}\theta +\text{cose}{{\text{c}}^{2}}\theta ={{(\sin \theta +\text{cosec}\theta )}^{2}}-2\sin \theta \text{ cosec}\theta \] \[={{(2)}^{2}}-2=4-2=2,\]since\[(\sin \theta +\text{cosec}\theta )=2.\]


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