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SSC Sample Paper Mock Test-5 SSC CGL Tear-II Paper-1

  • question_answer
    Which of the following statements are correct? I. \[\sin \,\,(2n+1)A\,\,sin\,\,A=si{{n}^{2}}\,\,(n+1)A-{{\sin }^{2}}nA\] II. \[{{\cos }^{2}}\,\,(45{}^\circ +x)-{{\sin }^{2}}\,\,(45{}^\circ -x)\] is independent III. \[\tan A=\frac{m}{m-1}\] and \[\tan B=\frac{1}{2m-1},\] then \[A-B=\frac{\pi }{4}\]

    A)  I and II

    B)  I and III

    C)  None of these   

    D)  All of these

    Correct Answer: A

    Solution :

    I. \[{{\sin }^{2}}\,\,(n+1)A-{{\sin }^{2}}nA\]
    \[=\sin \,\,[(n+1)A+n\,A]\sin \,\,[(n+1)A-nA]\]
    \[[\because {{\sin }^{2}}A-{{\sin }^{2}}B=\sin \,\,(A+B)\sin \,\,(A-B)]\]
    \[=\sin \,\,(2n+1)A\sin A\]
    II. \[{{\cos }^{2}}\,\,(45{}^\circ +x)-{{\sin }^{2}}(45{}^\circ -x)\]
    \[=\cos \,\,(45{}^\circ +x+45{}^\circ -x)\cos (45{}^\circ +x-45{}^\circ +x)\]
    \[[\because {{\cos }^{2}}A-{{\sin }^{2}}B=\cos \,\,(A+B)\cos \,\,(A-B)]\]
    \[=\cos 90{}^\circ \cdot \cos 2x=0\]
    Which is independent of x.
                           


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