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

  • question_answer
    If \[{{\sin }^{2}}\theta =\frac{{{x}^{2}}+{{y}^{2}}+1}{2x}\], then x must be  [UPSEAT 2004]

    A) - 3

    B) - 2

    C) 1

    D) None of these

    Correct Answer: D

    Solution :

    \[{{\sin }^{2}}\theta \le 1\] \\[\frac{{{x}^{2}}+{{y}^{2}}+1}{2x}\le 1\] \[{{x}^{2}}+{{y}^{2}}-2x+1\le 0\]. \[{{(x-1)}^{2}}+{{y}^{2}}\le 0\] It is possible, iff \[x=1\] and \[y=0\], i.e., It also depends on value of y. Hence, option (d) is correct.


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