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  • The value of cot⁡(π/4+θ) cot⁡(π/4-θ) is A. –1 B. 0 C. 1 D. Not defined

Q: 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

Answers (1)

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

Correct answer is option C.

Posted by

infoexpert21

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