Trigonometric Identities Question 367
Question: If $ A+B=225{}^\circ , $ then $ \frac{\cot A}{1+\cot A}.\frac{\cot B}{1+\cot B}= $
[MNR 1974]
Options:
A) 1
B) - 1
C) 0
D) 1/2
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{\cot A}{1+\cot A},.,\frac{\cot B}{1+\cot B}=\frac{1}{(1+\tan A),(1+\tan B)} $ $ =\frac{1}{\tan A+\tan B+1+\tan A\tan B} $ $ [\because ,\tan (A+B)=\tan 225^{o}] $
$ \Rightarrow ,\tan ,A+\tan ,B=1-\tan ,A,\tan B] $ $ =\frac{1}{1-\tan A,\tan B+1+\tan A\tan B}=\frac{1}{2} $ .
BETA
