Question

The value of $cot\left(\frac{\pi }{4}+\theta \right)cot\left(\frac{\pi }{4}-\theta \right)$ is

• A. $-1$
• B. $0$
• C. $1$
• D. Not defined

Answer 1

Answer: (C)

Given, $cot\left(\frac{\pi }{4}+\theta \right)cot\left(\frac{\pi }{4}-\theta \right)$
$=\frac{cot\frac{\pi }{4}cot\theta -1}{cot\frac{\pi }{4}+cot\theta }\times \frac{cot\frac{\pi }{4}cot\theta +1}{cot\theta -cot\frac{\pi }{4}}$
$=\frac{cot\theta -1}{1+cot\theta }\times \frac{1+cot\theta }{cot\theta -1}=1$