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SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (I)

  • question_answer
    If \[x\,\sin 45{}^\circ =y\,\text{cosec}\,30{}^\circ ,\]then \[\frac{{{x}^{4}}}{{{y}^{4}}}\] is equal to

    A) \[{{4}^{3}}\]

    B) \[{{6}^{3}}\]

    C) \[{{2}^{3}}\]

    D) \[{{8}^{3}}\]

    Correct Answer: A

    Solution :

    [a] \[x\sin 45{}^\circ =y\,\text{cosec}30{}^\circ \] \[\Rightarrow \]   \[\frac{x}{y}=\frac{\text{cosec}30{}^\circ }{\sin 45{}^\circ }=\frac{2}{\frac{1}{\sqrt{2}}}=2\sqrt{2}\] \[\Rightarrow \]   \[\frac{{{x}^{4}}}{{{y}^{4}}}={{(2\sqrt{2})}^{4}}=64={{4}^{3}}\]


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