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Question
The value of `cot(pi/4 + theta)cot(pi/4 - theta)` is ______.
Options
-1
0
1
Not defined
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Solution
The value of `cot(pi/4 + theta)cot(pi/4 - theta)` is 1.
Explanation:
`cot(pi/4 + theta)cot(pi/4 - theta) = (cot pi/4 cot theta - 1)/(cot theta + cot pi/4) xx (cot pi/4 cot theta + 1)/(cot theta - cot pi/4)`
= `(1cot theta - 1)/(cot theta + 1) xx (1cottheta + 1)/(cot theta - 1)`
= `(cot theta - 1)/(cot theta + 1) xx (cot theta + 1)/(cot theta - 1)`
= 1
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