11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[\frac{3\pi }{4}<\alpha <\pi ,\]then \[\sqrt{\text{cose}{{\text{c}}^{2}}\alpha +2\cot \alpha }\] is equal to  [Pb. CET 2000; AMU 2001; MP PET 2004]

    A) \[1+\cot \alpha \]

    B) \[1-\cot \alpha \]

    C) \[-1-\cot \alpha \]

    D) \[-1+\cot \alpha \]

    Correct Answer: C

    Solution :

    \[\sqrt{\text{cose}{{\text{c}}^{2}}\alpha +2\cot \alpha }=\sqrt{1+{{\cot }^{2}}\alpha +2\cot \alpha }=\,\,|1+\cot \alpha |\] But \[\frac{3\pi }{4}<\alpha <\pi \Rightarrow \cot \alpha <-1\Rightarrow 1+\cot \alpha <0\] Hence, \[|1+\cot \alpha |=-(1+\cot \alpha )\].


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