Trigonometric Identities Question 194
Question: If $ y=(1+tan,A)(1-tan,B), $ where A-B= $ \frac{\pi }{4} $ , then $ {{(y+1)}^{y+1}} $ is equal to
Options:
A) 9
B) 4
C) 27
D) 81
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ A-B=\frac{\pi }{4} $ or tan (A-B)= $ \tan \frac{\pi }{4} $ Or $ \frac{\tan A-\tan B}{1+\tan A\tan B}=1 $ Or $ \tan A-\tan B-\tan A\tan B=1 $ Or $ \tan A-\tan B-\tan A\tan B+1=2 $ Or $ (1+tanA)(1-tanB)=2\Rightarrow y=2 $ Hence, $ {{(y+1)}^{y+1}}={{(2+1)}^{2+1}}={{(3)}^{3}}=27 $
BETA
