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Question
For all real values of x, \[\cot x - 2 \cot 2x\] is equal to
Options
- \[\tan 2x\]
- \[\tan x\]
- \[- \cot 3x\]
none of these
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Solution
\[\text{ We have } , \]
\[\text{ cot } x - 2\cot 2x = \text{ cot } x - 2\frac{\cot^2 x - 1}{2\text{ cot } x}\]
\[ = \frac{\cot^2 x - \cot^2 x + 1}{\text{ cot } x}\]
\[ = \frac{1}{\text{ cot } x}\]
\[ = \text{ tan } x\]
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