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SSC Quantitative Aptitude Trigonometry Question Bank Trigonometry (I)

  • question_answer
    If\[\sin A+{{\sin }^{2}}A=1,\]then the value \[{{\cos }^{2}}A+{{\cos }^{4}}A\]is [SSC CGL Tier II, 2015]

    A) 2

    B) 1

    C)  \[1\frac{2}{3}\]

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

    Correct Answer: B

    Solution :

    [b] \[\sin A+{{\sin }^{2}}A=1\]\[\Rightarrow \]\[\sin A=1-{{\sin }^{2}}A\]             \[\therefore \]\[\sin A={{\cos }^{2}}A\] Then, \[{{\cos }^{2}}A+{{\cos }^{4}}A={{\cos }^{2}}A+{{(co{{s}^{2}}A)}^{2}}\] \[=\sin A+{{\sin }^{2}}A=1\]


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