SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (I)

  • question_answer
    If \[(\sin \theta -\cos \theta )=0,\]then,\[({{\sin }^{4}}\theta -{{\cos }^{4}}\theta )\]is equal to

    A) \[1\]

    B) \[\frac{1}{2}\]

    C) \[\frac{1}{4}\]

    D) \[\frac{3}{4}\]

    Correct Answer: B

    Solution :

    [b] \[\therefore \]\[\sin \theta -\cos \theta =0\]\[\Rightarrow \]\[\tan \theta =1\] \[\Rightarrow \]   \[\theta =45{}^\circ \]               \[\therefore \]\[(si{{n}^{4}}\theta +co{{s}^{4}}\theta )\] \[={{\left( \frac{1}{\sqrt{2}} \right)}^{4}}+{{\left( \frac{1}{\sqrt{2}} \right)}^{4}}\] =\[\left( \frac{1}{4}+\frac{1}{4} \right)=\frac{2}{4}=\frac{1}{2}\]


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