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SSC Sample Paper SSC-CGL TIER - I Sample Test Paper-4

  • question_answer
    Consider the following: \[\frac{\cot {{30}^{\circ }}+1}{\cot {{30}^{\circ }}-1}=2(\cos {{30}^{\circ }}+1)\] 2 sin \[{{45}^{\circ }}\]cos \[{{45}^{\circ }}\]- tan \[{{45}^{\circ }}\]cot \[{{45}^{\circ }}\]= 0 Which of the above identities is/are correct?

    A) Only 1              

    B) Only 2

    C) Both 1 and 2                 

    D) Neither 1 nor 2

    Correct Answer: C

    Solution :

    Statement I \[\frac{\cot {{30}^{\circ }}+1}{\cot {{30}^{\circ }}-1}=(\cos {{30}^{\circ }}+1)\] \[\frac{\sqrt{3}+1}{\sqrt{3}-1}=2\left( \frac{\sqrt{3}}{2}+1 \right)\] \[\Rightarrow \,\,\,\,\,\,\,\frac{\sqrt{3}+1}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}=\left( \frac{\sqrt{3}+2}{2} \right)\] \[\Rightarrow \,\,\,\,\,\,\,\frac{3+1+2\sqrt{3}}{3-1}=\sqrt{3}+2\] \[\Rightarrow \,\,\,\,\,\,\frac{2(2+\sqrt{3})}{2}=\sqrt{3}+2\] \[\Rightarrow \,\,\,\,\,\,\sqrt{3}+2=\sqrt{3}+2\] \[\therefore \]  It is true. Statement II:- \[2sin45{}^\circ  cos45{}^\circ  - tan45{}^\circ  cot45{}^\circ  = 0\] or,   \[2\times \left( \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}} \right)-1\times 1=0\] or,   \[2\times \frac{1}{2}-1\times 1=0\,;\,1-1=\] 0 \[\therefore \] Both statements I and II are true.


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