SATHEE: Quantitative Aptitude Ques 2143

Quantitative Aptitude Ques 2143

Question: If $ (1+\tan A)(1+\tan B)=2, $ then $ (A+B) $ is equal to

Options:

A) $ \frac{\pi }{2} $

B) $ \frac{\pi }{3} $

C) $ \frac{\pi }{4} $

D) $ \frac{\pi }{6} $

E) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

Given, $ 1+\tan A+\tan B+\tan A\tan B=2 $

$ \Rightarrow $ $ \tan A+\tan B=1-\tan A\tan B $

$ \Rightarrow $ $ \frac{\tan A+\tan B}{1-\tan AtanB}=1=\tan 45{}^\circ $

$ \Rightarrow $ $ \tan (A+B)=\tan 45{}^\circ $ $ [ \because \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B} ] $

$ \therefore $ $ A+B=45{}^\circ =\frac{\pi }{4} $

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Quantitative Aptitude Ques 2143

Question: If $ (1+\tan A)(1+\tan B)=2, $ then $ (A+B) $ is equal to

Options:

Answer:

Solution:

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