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If $\tan 40 ° + 2 \tan 10 ° = \cot x$ then $x =$

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75 °

85 °

30 °

40 °

answer is D.

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Detailed Solution

\tan 40 ° + 2 \tan 10 ° = \cot x

$\Rightarrow \tan 40 ° + \tan 10 ° + \tan 10 ° = \cot x$

$\Rightarrow \tan 40 ° + \cot 80 ° + \cot 80 ° = \cot x$

$\Rightarrow \tan 40 ° + 2 \cot 80 ° = \cot x$

$\Rightarrow \tan 40 ° + \cot 40 ° - \tan 40 ° = \cot x$ $(∵ 2 \cot A = \cot \frac{A}{2} - \tan \frac{A}{2})$

$\Rightarrow \cot 40 ° = \cot x$

$x = 40 °$

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