Trigonometric Equations Question 265
Question: If in a triangle ABC, angle C is $ 45^{o} $ , then $ (1+\cot A)(1+\cot B)= $
[Kurukshetra CEE 1998]
Options:
A) -1
B) 2
C) 3
D) $ 1/\sqrt{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- Given, $ \angle C=45^{o} $ \ $ A+B=180^{o}-45^{o}=135^{o} $ \ $ \cot (A+B)=\frac{\cot A\cot B-1}{\cot A+\cot B} $
Þ $ \cot (135^{o})=-1=\frac{\cot A\cot B-1}{\cot A+\cot B} $
Þ $ \cot A+\cot B=1-\cot A\cot B $ $ 1+\cot A+\cot B+\cot A\cot B=2 $
Þ $ (1+\cot A)(1+\cot B)=2 $ .
BETA
