Quantitative Aptitude Ques 177

Question: $ \frac{\tan A+\tan B}{\cot A+\cot ,B} $ is equal to

Options:

A) $ \cot A,\cot B $

B) $ \sec A,cosec,B $

C) $ \tan A,\tan B $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ \frac{\tan A+\tan B}{\cot A+\cot B}=\frac{\tan A+\tan B}{\frac{1}{\tan A}+\frac{1}{\tan B}} $ $ =\frac{\tan B+\tan B}{\frac{\tan B+\tan A}{\tan A\cdot \tan B}}=\frac{1}{\frac{1}{\tan A\cdot \tan B}} $ $ =\tan A\cdot \tan B $
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