Assertion , Reason

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Both Assertion and Reason are correct and reason is the correct explanation of Assertion

Both Assertion and Reason are correct and reason is NOT the correct explanation of Assertion

Assertion is correct but the reason is INCORRECT

Both Assertion and Reason are INCORRECT

answer is A.

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Detailed Solution

Assertion (A): $\tan 40 ° + \tan 80 ° - \sqrt{3} \tan 40 ° \cdot \tan 80 ° = - \sqrt{3}$

$= \tan 40 ° + \tan 80 ° - \sqrt{3} (1 - \tan 40 \cdot \tan 80)$

$\Rightarrow \frac{\tan 40 + \tan 80}{1 - \tan 40 \cdot \tan 80} = - \sqrt{3}$

$\Rightarrow \tan (40 + 80) = - \sqrt{3} \Rightarrow \tan (120) = - \sqrt{3}$

$\Rightarrow \tan (90 + 30) = - \sqrt{3}$ $\Rightarrow - \cot 30 = - \sqrt{3}$

Reason (R): $\tan (A + B) = \tan A + \tan B + \tan (A + B) \cdot \tan A \cdot \tan B$

$\Rightarrow \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \cdot \tan B}$

$\Rightarrow (1 - \tan A \cdot \tan B) \cdot \tan (A + B) = \tan A + \tan B$

$\Rightarrow \tan (A + B) - \tan (A + B) \cdot \tan A \cdot \tan B = \tan A + \tan B$

$\Rightarrow \tan (A + B) = \tan A + \tan B + \tan (A + B) \cdot \tan A \cdot \tan B$

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