Aspire Faculty ID #15268 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

The value of $\tan1^{\circ} \cdot \tan2^{\circ} \cdot \tan3^{\circ} \cdots \tan89^{\circ}$ is …

Solution

$\tan1^{\circ} \cdot \tan89^{\circ} = \tan1^{\circ} \cdot \cot1^{\circ} = 1$. Similarly, $\tan2^{\circ} \cdot \tan88^{\circ} = 1$, and so on. But $\tan45^{\circ} = 1$. Hence the entire product = 1.
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