SATHEE: Quantitative Aptitude Ques 1128

Quantitative Aptitude Ques 1128

Question: If $ \tan 15{}^\circ =2-\sqrt{3}, $ then the value of $ \tan 15{}^\circ \cot 75{}^\circ +\tan 75{}^\circ \cot 15{}^\circ $ is

Options:

A) 14

B) 12

C) 10

D) 8

Show Answer

Answer:

Correct Answer: A

Solution:

Given, $ \tan 15{}^\circ =2-\sqrt{3} $ Then, $ \tan 15{}^\circ \cdot \cot 75{}^\circ +tan75{}^\circ \cdot cot15{}^\circ $ $ =\tan 15{}^\circ \cdot \cot (90{}^\circ -15{}^\circ )+\tan (90{}^\circ -15{}^\circ )\cdot \cot 15{}^\circ $ $ ={{\tan }^{2}}15{}^\circ +{{\cot }^{2}}15{}^\circ $ (i) $ [\because \tan (90{}^\circ -\theta )=\cot \theta ,\cot (90{}^\circ -\theta )=\tan \theta ] $ Now, $ \tan 15{}^\circ =2-\sqrt{3} $

$ \Rightarrow $ $ \cot 15{}^\circ =\frac{1}{2-\sqrt{3}}=\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})} $ $ =2+\sqrt{3} $ [on rationalisation]

$ \therefore $ $ {{\tan }^{2}}15{}^\circ +{{\cot }^{2}}15{}^\circ ={{(2-\sqrt{3})}^{2}}+{{(2+\sqrt{3})}^{2}} $ $ =[4+3-4\sqrt{3}]+[4+3+4\sqrt{3}] $ $ =7+7=14 $

Quantitative Aptitude Ques 1127

Quantitative Aptitude Ques 1129

Quantitative Aptitude Ques 1128

Question: If $ \tan 15{}^\circ =2-\sqrt{3}, $ then the value of $ \tan 15{}^\circ \cot 75{}^\circ +\tan 75{}^\circ \cot 15{}^\circ $ is

Options:

Answer:

Solution:

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