Quantitative Aptitude Ques 1502

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

Options:

A) $ \cot A\cot B $

B) $ \sec A\text{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{\frac{\sin A}{\cos A}+\frac{\sin B}{\cos B}}{\frac{\cos A}{\sin A}+\frac{\cos B}{\sin B}} $ $ =\frac{\frac{\sin A\cdot \cos B+\cos A\cdot \sin B}{\cos A\cdot \cos B}}{\frac{\cos A\cdot \sin B+\sin A\cdot \cos B}{\sin A\cdot \sin B}} $ $ =\frac{\sin A\cdot \sin B}{\cos A\cdot \cos B}=\tan A\cdot \tan B $
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