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

  • question_answer
    The equation \[{{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta \]is possible only when

    A) \[2a=b\]

    B) \[a=b\]

    C) \[a=2b\]

    D) None of these

    Correct Answer: B

    Solution :

    We have \[{{(a+b)}^{2}}=4ab{{\sin }^{2}}\theta \] \[\Rightarrow {{\sin }^{2}}\theta =\frac{{{(a+b)}^{2}}}{4ab}\le 1\Rightarrow {{(a+b)}^{2}}-4ab\le 0\] \[\Rightarrow {{(a-b)}^{2}}\le 0\Rightarrow a=b.\]


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