11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If \[1+\cos \alpha +{{\cos }^{2}}\alpha +.......\,\infty =2-\sqrt{2,}\] then \[\alpha ,\] \[(0<\alpha <\pi )\] is    [Roorkee 2000; AMU 2005]

    A) \[\pi /8\]

    B) \[\pi /6\]

    C) \[\pi /4\]

    D) \[3\pi /4\]

    Correct Answer: D

    Solution :

    \[1-\cos \alpha =\frac{1}{2-\sqrt{2}}=1+\frac{1}{\sqrt{2}}\] Þ\[\cos \alpha =-\frac{1}{\sqrt{2}}=\cos \frac{3\pi }{4}\] Þ \[\alpha =\frac{3\pi }{4}\].


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