A) 0
B) \[-1\]
C) 1
D) \[-2\]
E) 2
Correct Answer: C
Solution :
\[\cot \left( \frac{\pi }{4}+\theta \right).\cot \left( \frac{\pi }{4}-\theta \right)\] and \[\theta \in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\tilde{\ }\left\{ \pm \frac{\pi }{4} \right\}\] \[=\tan \left( \frac{\pi }{2}-\frac{\pi }{4}-\theta \right).\tan \left( \frac{\pi }{2}-\frac{\pi }{4}+\theta \right)\] \[=\tan \left( \frac{\pi }{4}-\theta \right).\tan \left( \frac{\pi }{4}+\theta \right)\] \[=\frac{\tan \frac{\pi }{4}-\tan \theta }{1+\tan \frac{\pi }{4}.\tan \theta }.\frac{\tan \frac{\pi }{4}+\tan \theta }{1-\tan \frac{\pi }{4}.\tan \theta }\] \[=\frac{1-\tan \theta }{1+\tan \theta }.\frac{1+\tan \theta }{1-\tan \theta }\]
You need to login to perform this action.
You will be redirected in
3 sec
