Trigonometric Identities Question 369
Question: If $ A+B=\frac{\pi }{4}, $ then $ (1+\tan A)(1+\tan B)= $
Options:
A) 1
B) 2
C) $ \infty $
D) -2
Show Answer
Answer:
Correct Answer: B
Solution:
Given that $ A+B=\frac{\pi }{4},\Rightarrow ,\tan ,(A+B)=\tan ,\frac{\pi }{4} $
$ \Rightarrow \frac{\tan A+\tan B}{1-\tan A,\tan B}=1 $
$ \Rightarrow \tan A+\tan B+\tan A,\tan B=1 $
$ \Rightarrow (1+\tan A),(1+\tan B)=2 $ .
BETA
